159 results on '"Giuseppe Marino"'
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2. Fixed point results for dominated mappings in rectangular b-metric spaces with applications
- Author
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Abdullah Shoaib, Tahair Rasham, Giuseppe Marino, and Jung Rye Lee
- Subjects
fixed point ,complete rectangular b-metric space ,α-dominated mapping ,ćirić type rational contraction condition ,partial order ,$\preceq$-dominated mapping ,graph dominated mapping ,Mathematics ,QA1-939 - Abstract
In this paper, we establish some fixed point results for α-dominated mappings fulfilling new generalized locally Ćirić type rational contraction conditions in complete rectangular b-metric space. As an application, we establish the existence of fixed point of $\preceq $-dominated mappings in an ordered complete rectangular b-metric space. The notion of graph dominated mappings is introduced. Fixed point results with graphic contractions for such mappings are established. more...
- Published
- 2020
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3. Sufficient conditions to solve two systems of integral equations via fixed point results
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Tahair Rasham, Abdullah Shoaib, Giuseppe Marino, Badriah A. S. Alamri, and Muhammad Arshad
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Fixed point ,Two families of multivalued mapping ,Dislocated b-metric space ,Application to the system of nonlinear integral equations ,Mathematics ,QA1-939 - Abstract
Abstract The purpose of this paper is to study the solution of two systems of nonlinear integral equations via fixed point results in a complete dislocated b-metric space. Also the notion of graphic contractions on a closed set for two families of graph dominated multivalued mappings is introduced. Our results generalize some previous results in the existing literature. more...
- Published
- 2019
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4. Common α-Fuzzy Fixed Point Results for F-Contractions with Applications
- Author
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Jamshaid Ahmad, Giuseppe Marino, and Saleh Abdullah Al-Mezel
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complete b-metric spaces ,F-contractions ,α-fuzzy mappings ,multivalued mappings ,Hukuhara derivative ,Mathematics ,QA1-939 - Abstract
F-contractions have inspired a branch of metric fixed point theory committed to the generalization of the classical Banach contraction principle. The study of these contractions and α-fuzzy mappings in b-metric spaces was attempted timidly and was not successful. In this article, the main objective is to obtain common α-fuzzy fixed point results for F-contractions in b-metric spaces. Some multivalued fixed point results in the literature are derived as consequences of our main results. We also provide a non-trivial example to show the validity of our results. As applications, we investigate the solution for fuzzy initial value problems in the context of a generalized Hukuhara derivative. Our results generalize, improve and complement several developments from the existing literature. more...
- Published
- 2021
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5. Strong convergence theorem for strict pseudo-contractions in Hilbert spaces
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Giuseppe Marino, Bruno Scardamaglia, and Erdal Karapinar
- Subjects
Mann’s iterations ,strict pseudo-contractions mappings ,variational inequalities ,Mainge’s lemma ,Mathematics ,QA1-939 - Abstract
Abstract In this paper, inspired by Hussain et al. (Fixed Point Theory Appl. 2015:17, 2015), we study a modified Mann method to approximate strongly fixed points of strict pseudo-contractive mappings. In (Hussain et al. in Fixed Point Theory Appl. 2015:17, 2015) it is shown that the same algorithm converges strongly to a fixed point of a nonexpansive mapping under suitable hypotheses on the coefficients. Here the assumptions on the coefficients are different, as well as the techniques of the proof. more...
- Published
- 2016
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6. Fixed Point Theorems for Generalized (αβ-ψ)-Contractions in F -Metric Spaces with Applications
- Author
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Saleh Abdullah Al-Mezel, Jamshaid Ahmad, and Giuseppe Marino
- Subjects
nonlinear neutral differential equation ,fixed point ,generalized (αβ-ψ)-contraction ,ℱ-metric spaces ,Mathematics ,QA1-939 - Abstract
The purpose of this paper is to define generalized ( α β - ψ ) -contraction in the context of F -metric space and obtain some new fixed point results. As applications, we solve a nonlinear neutral differential equation with an unbounded delay ϑ / ( ι ) = − ρ 1 ( ι ) ϑ ( ι ) + ρ 2 ( ι ) L ( ϑ ( ι − ς ( ι ) ) ) + ρ 3 ( ι ) ϑ / ( ι − ς ( ι ) ) , where ρ 1 ( ι ) , ρ 2 ( ι ) are continuous, ρ 3 ( ι ) is continuously differentiable and ς ( ι ) > 0 , for all ι ∈ R and is twice continuously differentiable. more...
- Published
- 2020
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7. Function Spaces, Fixed Points, Approximations, and Applications
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Giuseppe Marino, Filomena Cianciaruso, Nawab Hussain, and Enrique Llorens Fuster
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Mathematics ,QA1-939 - Published
- 2017
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8. Fixed Points for a Pair of F-Dominated Contractive Mappings in Rectangular b-Metric Spaces with Graph
- Author
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Tahair Rasham, Giuseppe Marino, and Abdullah Shoaib
- Subjects
fixed point ,generalized F-contraction ,α*-dominated mapping ,graphic contractions ,Mathematics ,QA1-939 - Abstract
Recently, George et al. (in Georgea, R.; Radenovicb, S.; Reshmac, K.P.; Shuklad, S. Rectangular b-metric space and contraction principles. J. Nonlinear Sci. Appl. 2015, 8, 1005–1013) furnished the notion of rectangular b-metric pace (RBMS) by taking the place of the binary sum of triangular inequality in the definition of a b-metric space ternary sum and proved some results for Banach and Kannan contractions in such space. In this paper, we achieved fixed-point results for a pair of F-dominated mappings fulfilling a generalized rational F-dominated contractive condition in the better framework of complete rectangular b-metric spaces complete rectangular b-metric spaces. Some new fixed-point results with graphic contractions for a pair of graph-dominated mappings on rectangular b-metric space have been obtained. Some examples are given to illustrate our conclusions. New results in ordered spaces, partial b-metric space, dislocated metric space, dislocated b-metric space, partial metric space, b-metric space, rectangular metric spaces, and metric space can be obtained as corollaries of our results. more...
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- 2019
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9. On Strong Convergence of Halpern’s Method for Quasi-Nonexpansive Mappings in Hilbert Spaces
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Jesus Garcia Falset, Enrique Llorens-Fuster, Giuseppe Marino, and Angela Rugiano
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approximation algorithm ,fixed point ,variational inequality ,Mathematics ,QA1-939 - Abstract
In this paper, we introduce a Halpern’s type method to approximate common fixed points of a nonexpansive mapping T and a strongly quasi-nonexpansive mappings S, defined in a Hilbert space, such that I − S is demiclosed at 0. The result shows as the same algorithm converges to different points, depending on the assumptions of the coefficients. Moreover, a numerical example of our iterative scheme is given. more...
- Published
- 2016
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10. On Mann’s Type Method for Nonexpansive and Strongly Quasinonexpansive Mappings in Hilbert Spaces
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Nawab Hussain, Giuseppe Marino, and Badriah A. S. Alamri
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Mathematics ,QA1-939 - Abstract
In the setting of Hilbert spaces, we study Mann’s type method to approximate strong solutions of variational inequalities. We show that these solutions are fixed points of a nonexpansive mapping and/or a strongly quasinonexpansive mapping, depending on the coefficients involved in the algorithm. more...
- Published
- 2015
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11. Iterative Methods and Applications 2014
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Giuseppe Marino, Filomena Cianciaruso, Claudio H. Morales, Luigi Muglia, and D. R. Sahu
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Mathematics ,QA1-939 - Published
- 2015
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12. Iterative Methods and Applications
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Giuseppe Marino, Filomena Cianciaruso, Luigi Muglia, Claudio H. Morales, and Daya Ram Sahu
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Mathematics ,QA1-939 - Published
- 2014
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13. On Mann’s Method with Viscosity for Nonexpansive and Nonspreading Mappings in Hilbert Spaces
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Nawab Hussain, Giuseppe Marino, and Afrah A. N. Abdou
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Mathematics ,QA1-939 - Abstract
In the setting of Hilbert spaces, inspired by Iemoto and Takahashi (2009), we study a Mann’s method with viscosity to approximate strongly (common) fixed points of a nonexpansive mapping and a nonspreading mapping. A crucial tool in our results is the nonspreading-average type mapping. more...
- Published
- 2014
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14. Applications of Fixed-Point and Optimization Methods to the Multiple-Set Split Feasibility Problem
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Yonghong Yao, Rudong Chen, Giuseppe Marino, and Yeong Cheng Liou
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Mathematics ,QA1-939 - Abstract
The multiple-set split feasibility problem requires finding a point closest to a family of closed convex sets in one space such that its image under a linear transformation will be closest to another family of closed convex sets in the image space. It can be a model for many inverse problems where constraints are imposed on the solutions in the domain of a linear operator as well as in the operator’s range. It generalizes the convex feasibility problem as well as the two-set split feasibility problem. In this paper, we will review and report some recent results on iterative approaches to the multiple-set split feasibility problem. more...
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- 2012
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15. Applications of Fixed Point and Approximate Algorithms
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Yonghong Yao, Rudong Chen, Giuseppe Marino, and Yeong-Cheng Liou
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Mathematics ,QA1-939 - Published
- 2012
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16. On the Convergence of Mann and Ishikawa Iterative Processes for Asymptotically ϕ-Strongly Pseudocontractive Mappings
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Xuewu Wang, Giuseppe Marino, and Luigi Muglia
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Mathematics ,QA1-939 - Abstract
We prove the equivalence and the strong convergence of (1) the modified Mann iterative process and (2) the modified Ishikawa iterative process for asymptotically ϕ-strongly pseudocontractive mappings in a uniformly smooth Banach space. more...
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- 2012
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17. Fixed-Point Theory, Variational Inequalities, and Its Approximation Algorithms
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Giuseppe Marino, Vittorio Colao, Yonghong Yao, Genaro López, and Enrique Llorens-Fuster
- Subjects
Mathematics ,QA1-939 - Published
- 2011
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18. On a Two-Step Algorithm for Hierarchical Fixed Point Problems and Variational Inequalities
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Filomena Cianciaruso, Giuseppe Marino, Luigi Muglia, and Yonghong Yao
- Subjects
Mathematics ,QA1-939 - Abstract
A common method in solving ill-posed problems is to substitute the original problem by a family of well-posed (i.e., with a unique solution) regularized problems. We will use this idea to define and study a two-step algorithm to solve hierarchical fixed point problems under different conditions on involved parameters. more...
- Published
- 2009
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19. Composition operators of summable functions spaces
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Virginia De Cicco and Giuseppe Marino
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Mathematics ,QA1-939 - Abstract
A composition operator is a linear operator CT on a subspace of KX by a point transformation T on a set X (where K denotes the scalar field) by the formula CT f(x) :=f ∘ T(x). We give some necessary and/or sufficient conditions under which the map T induces a continuous composition operator on suitable topological subspaces of summable functions of KX as Lp or W1,p. more...
- Published
- 1989
20. COMBINING SUBSPACE CODES
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Sascha Kurz, Giuseppe Marino, Antonio Cossidente, Francesco Pavese, Cossidente, A., Kurz, S., Marino, G., and Pavese, F.
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constant-dimension subspace code ,FOS: Computer and information sciences ,Computer Networks and Communications ,Computer Science - Information Theory ,Context (language use) ,0102 computer and information sciences ,02 engineering and technology ,01 natural sciences ,Microbiology ,Combinatorics ,FOS: Mathematics ,0202 electrical engineering, electronic engineering, information engineering ,Discrete Mathematics and Combinatorics ,Mathematics - Combinatorics ,finite projective geometry ,Mathematics ,Algebra and Number Theory ,Information Theory (cs.IT) ,Applied Mathematics ,Primary 51E20, Secondary 05B25, 94B65 ,Order (ring theory) ,020206 networking & telecommunications ,Finite projective geometry ,network coding ,Linear subspace ,010201 computation theory & mathematics ,Combinatorics (math.CO) ,Subspace topology ,Constant–dimension subspace code - Abstract
In the context of constant--dimension subspace codes, an important problem is to determine the largest possible size $A_q(n, d; k)$ of codes whose codewords are $k$-subspaces of $\mathbb{F}_q^n$ with minimum subspace distance $d$. Here in order to obtain improved constructions, we investigate several approaches to combine subspace codes. This allow us to present improvements on the lower bounds for constant--dimension subspace codes for many parameters, including $A_q(10, 4; 5)$, $A_q(12, 4; 4)$, $A_q(12, 6, 6)$ and $A_q(16, 4; 4)$., 17 pages; construction for A_(10,4;5) was flawed more...
- Published
- 2023
21. Object similarity measures and Pawlak’s indiscernibility on decision tables
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Giuseppe Marino, Federico Infusino, Giampiero Chiaselotti, and Francesca Catanzariti
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Pure mathematics ,Class (set theory) ,Information Systems and Management ,05 social sciences ,050301 education ,02 engineering and technology ,Similarity measure ,Object (computer science) ,Computer Science Applications ,Theoretical Computer Science ,Set (abstract data type) ,Similarity (network science) ,Artificial Intelligence ,Control and Systems Engineering ,0202 electrical engineering, electronic engineering, information engineering ,020201 artificial intelligence & image processing ,Focus (optics) ,Decision table ,0503 education ,Software ,Mathematics ,Unit interval - Abstract
In this paper we investigate the mathematical foundations of the notion of similarity between objects in relation to the granulations on a decision table D . First of all, we compare the endogenous granulation induced by Pawlak’s indiscernibility with the exogenous granulation induced by a similarity measure ζ defined on pairs of objects and assuming values in the unit interval. To this aim, the starting point of our analysis is the introduction of the notion of refinement of the granulation induced by an attribute subset A through the object similarity measure ζ . More in detail, we say that ζ refines the granulation induced by A if ζ assumes value 1 on a pair of objects if and only if they are A-indiscernible. Next, starting from two given families ρ and ν of numerical maps defined on pairs of admissible values of D , we determine a broad class of potential similarity measures on the objects of D refining, sometimes under some specific additional hypotheses, the A-granulation on the object set of D . With regard to a such class of similarity measures, we establish several mathematical properties. Finally, we focus our attention to the analysis of specific pairs of numerical maps ρ and ν that have been classically studied in literature and, for each of them, we exhibit the main properties with respect to the aforementioned refinement of granulation. more...
- Published
- 2020
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22. MRD-codes arising from the trinomial xq+xq3+cxq5∈Fq6[x]
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Giuseppe Marino, Ferdinando Zullo, and Maria Montanucci
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Combinatorics ,Numerical Analysis ,Algebra and Number Theory ,Dimension (vector space) ,010102 general mathematics ,Minimum distance ,Discrete Mathematics and Combinatorics ,010103 numerical & computational mathematics ,Geometry and Topology ,0101 mathematics ,Trinomial ,01 natural sciences ,Mathematics - Abstract
In [10] , the existence of F q -linear MRD-codes of F q 6 × 6 , with dimension 12, minimum distance 5 and left idealiser isomorphic to F q 6 , defined by a trinomial of F q 6 [ x ] , when q is odd and q ≡ 0 , ± 1 ( mod 5 ) , has been proved. In this paper we show that this family produces F q -linear MRD-codes of F q 6 × 6 , with the same properties, also in the remaining q odd cases, but not in the q even case. These MRD-codes are not equivalent to the previously known MRD-codes. We also prove that the corresponding maximum scattered F q -linear sets of PG ( 1 , q 6 ) are not P Γ L ( 2 , q 6 ) -equivalent to any previously known linear set. more...
- Published
- 2020
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23. On fixed point results for α∗- ψ- dominated fuzzy contractive mappings with graph
- Author
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Aqeel Shazad, Tahair Rasham, Giuseppe Marino, and Abdullah Shoaib
- Subjects
Statistics and Probability ,Combinatorics ,Artificial Intelligence ,General Engineering ,Graph (abstract data type) ,Fixed point ,Fuzzy logic ,Mathematics - Published
- 2020
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24. On regular systems of finite classical polar spaces
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Francesco Pavese, Valentino Smaldore, Antonio Cossidente, Giuseppe Marino, Cossidente, A., Marino, G., Pavese, F., and Smaldore, V.
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Set (abstract data type) ,Combinatorics ,FOS: Mathematics ,Mathematics - Combinatorics ,Discrete Mathematics and Combinatorics ,Projective space ,Polar ,Combinatorics (math.CO) ,Polar space ,Rank (differential topology) ,Mathematics - Abstract
Let P be a finite classical polar space of rank d . An m -regular system with respect to ( k − 1 ) -dimensional projective spaces of P , 1 ≤ k ≤ d − 1 , is a set R of generators of P with the property that every ( k − 1 ) -dimensional projective space of P lies on exactly m generators of R . Regular systems of polar spaces are investigated. Some non-existence results about certain 1-regular systems of polar spaces with low rank are proved and a procedure to obtain m ′ -regular systems from a given m -regular system is described. Finally, three different construction methods of regular systems w.r.t. points of various polar spaces are discussed. more...
- Published
- 2022
25. Orbit codes from forms on vector spaces over a finite field
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Alessandro Siciliano, Giuseppe Marino, Antonio Cossidente, Francesco Pavese, Angela Aguglia, Aguglia, A., Cossidente, A., Marino, G., Pavese, F., and Siciliano, A.
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Automorphism group ,Algebra and Number Theory ,Computer Networks and Communications ,Applied Mathematics ,Orbit code ,020206 networking & telecommunications ,General linear group ,0102 computer and information sciences ,02 engineering and technology ,Bilinear form ,01 natural sciences ,Microbiology ,Hermitian matrix ,Combinatorics ,Finite field ,010201 computation theory & mathematics ,Subspace code ,Constant dimension code ,0202 electrical engineering, electronic engineering, information engineering ,Discrete Mathematics and Combinatorics ,Orbit (control theory) ,Vector space ,Mathematics - Abstract
In this paper we construct different families of orbit codes in the vector spaces of the symmetric bilinear forms, quadratic forms and Hermitian forms on an \begin{document}$ n $\end{document}-dimensional vector space over the finite field \begin{document}$ {\mathbb F_{q}} $\end{document}. All these codes admit the general linear group \begin{document}$ {{{{\rm{GL}}}}}(n,q) $\end{document} as a transitive automorphism group. more...
- Published
- 2022
26. Boundary Point Method and the Mann–Dotson Algorithm for Non-self Mappings in Banach Spaces
- Author
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Giuseppe Marino and Luigi Muglia
- Subjects
010101 applied mathematics ,Weak convergence ,General Mathematics ,010102 general mathematics ,Banach space ,Regular polygon ,Function (mathematics) ,0101 mathematics ,Fixed point ,Lambda ,01 natural sciences ,Algorithm ,Mathematics - Abstract
Let C be a closed, convex and nonempty subset of a Banach space X. Let $${T : C \rightarrow X}$$ be a nonexpansive inward mapping. We consider the boundary point map $${h_{C,T } : C \rightarrow \mathbb{R}}$$ depending on C and T defined by $${h_{C,T} = {\rm max}\{\lambda \in [0,1] : [(1-\lambda)x + \lambda Tx] \in C\}}$$ , for all $${x \in C}$$ . Then for a suitable step-by-step construction of the control coefficients by using the function $${h_{C,T }}$$ , we show the convergence of the Mann-Dotson algorithm to a fixed point of T. We obtain strong convergence if $${\sum\limits_{n \in \mathbb{N}} \alpha_{n} < \infty}$$ and weak convergence if $${\sum\limits_{n \in \mathbb{N}} \alpha_{n} = \infty}$$ . more...
- Published
- 2019
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27. Boundary Point Method and Mann-Dotson’s Algorithm for Nonself Strict Pseudo-contractive Mappings in Uniformly Smooth Banach Spaces
- Author
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Luigi Muglia and Giuseppe Marino
- Subjects
Pure mathematics ,Control and Optimization ,Signal Processing ,Banach space ,Analysis ,Computer Science Applications ,Mathematics - Published
- 2019
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28. Some Results on the Approximation of Solutions of Variational Inequalities for Multivalued Maps on Banach Spaces
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Luigi Muglia and Giuseppe Marino
- Subjects
010101 applied mathematics ,Set (abstract data type) ,Pure mathematics ,General Mathematics ,010102 general mathematics ,Variational inequality ,Banach space ,0101 mathematics ,Fixed point ,Focus (optics) ,01 natural sciences ,Mathematics - Abstract
Multivalued $$*$$ ∗ -nonexpansive mappings are studied in Banach spaces. The demiclosedness principle is established. Here we focus on the problem of solving a variational inequality which is defined on the set of fixed points of a multivalued $$*$$ ∗ -nonexpansive mapping. For this purpose, we introduce two algorithms approximating the unique solution of the variational inequality. more...
- Published
- 2021
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29. Fixed point results for a pair of fuzzy mappings and related applications in b-metric like spaces
- Author
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Abdullah Shoaib, Choonkill Park, Giuseppe Marino, Aqeel Shahzad, and Tahair Rasham
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Algebra and Number Theory ,Partial differential equation ,Semi α ∗ $\alpha _{\ast }$ -dominated fuzzy mappings ,Applied Mathematics ,010102 general mathematics ,Functional equations ,Fixed point ,01 natural sciences ,Fuzzy logic ,010101 applied mathematics ,Algebra ,Dynamic programming ,Graphic contractions ,Bounded function ,Metric (mathematics) ,Functional equation ,QA1-939 ,0101 mathematics ,Integral equations ,Realization (systems) ,Mathematics ,Analysis - Abstract
This paper is devoted to finding out some realization of the concept of b-metric like space. First, we attain a fixed point for two fuzzy mappings satisfying a suitable requirement of contractiveness. Subsequently, we apply such a result to graphic contractions. Also, we attain a unique solution for a system of integral equations, and lastly we give an application to ensure that there exists a common bounded solution of a suitable functional equation in dynamic programming. more...
- Published
- 2021
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30. Common α-Fuzzy Fixed Point Results for F-Contractions with Applications
- Author
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Giuseppe Marino, Saleh Abdullah Al-Mezel, and Jamshaid Ahmad
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Pure mathematics ,Generalization ,General Mathematics ,lcsh:Mathematics ,Hukuhara derivative ,010102 general mathematics ,Fixed-point theorem ,Context (language use) ,α-fuzzy mappings ,Fixed point ,lcsh:QA1-939 ,multivalued mappings ,01 natural sciences ,Fuzzy logic ,010101 applied mathematics ,F-contractions ,Computer Science (miscellaneous) ,Initial value problem ,Computer Science::Programming Languages ,complete b-metric spaces ,0101 mathematics ,Contraction principle ,Engineering (miscellaneous) ,Complement (set theory) ,Mathematics - Abstract
F-contractions have inspired a branch of metric fixed point theory committed to the generalization of the classical Banach contraction principle. The study of these contractions and α-fuzzy mappings in b-metric spaces was attempted timidly and was not successful. In this article, the main objective is to obtain common α-fuzzy fixed point results for F-contractions in b-metric spaces. Some multivalued fixed point results in the literature are derived as consequences of our main results. We also provide a non-trivial example to show the validity of our results. As applications, we investigate the solution for fuzzy initial value problems in the context of a generalized Hukuhara derivative. Our results generalize, improve and complement several developments from the existing literature. more...
- Published
- 2021
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31. Generalising the Scattered Property of Subspaces
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Ferdinando Zullo, Bence Csajbók, Giuseppe Marino, Olga Polverino, Csajbok, B., Marino, G., Polverino, O., and Zullo, F.
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scattered subspace, MRD-code ,Strongly regular graph ,010102 general mathematics ,Dimension (graph theory) ,0102 computer and information sciences ,01 natural sciences ,Upper and lower bounds ,Linear subspace ,Duality relation ,05B25, 51E20, 33C20 ,Combinatorics ,Computational Mathematics ,Hyperplane ,010201 computation theory & mathematics ,FOS: Mathematics ,Mathematics - Combinatorics ,MRD-code ,Discrete Mathematics and Combinatorics ,Combinatorics (math.CO) ,0101 mathematics ,scattered subspace ,Mathematics ,Vector space - Abstract
Let $V$ be an $r$-dimensional $\mathbb{F}_{q^n}$-vector space. We call an $\mathbb{F}_q$-subspace $U$ of $V$ $h$-scattered if $U$ meets the $h$-dimensional $\mathbb{F}_{q^n}$-subspaces of $V$ in $\mathbb{F}_q$-subspaces of dimension at most $h$. In 2000 Blokhuis and Lavrauw proved that $\dim_{\mathbb{F}_q} U \leq rn/2$ when $U$ is $1$-scattered. Subspaces attaining this bound have been investigated intensively because of their relations with projective two-weight codes and strongly regular graphs. MRD-codes with a maximum idealiser have also been linked to $rn/2$-dimensional $1$-scattered subspaces and to $n$-dimensional $(r-1)$-scattered subspaces. In this paper we prove the upper bound $rn/(h+1)$ for the dimension of $h$-scattered subspaces, $h>1$, and construct examples with this dimension. We study their intersection numbers with hyperplanes, introduce a duality relation among them, and study the equivalence problem of the corresponding linear sets., We implemented the referees comments and changed the title. To appear in Combinatorica more...
- Published
- 2021
32. New maximum scattered linear sets of the projective line
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Giuseppe Marino, Bence Csajbók, Ferdinando Zullo, Csajbok, B., Marino, G., and Zullo, F.
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Scattered subspace ,Algebra and Number Theory ,Applied Mathematics ,010102 general mathematics ,Minimum distance ,General Engineering ,0102 computer and information sciences ,Linear set, MRD-code, Scattered subspace ,Trinomial ,51E20, 51E22, 05B25 ,01 natural sciences ,Linear subspace ,Theoretical Computer Science ,Combinatorics ,010201 computation theory & mathematics ,Projective line ,FOS: Mathematics ,Mathematics - Combinatorics ,MRD-code ,Combinatorics (math.CO) ,0101 mathematics ,Equivalence (formal languages) ,Linear set ,Mathematics - Abstract
In [2] and [18] are presented the first two families of maximum scattered F q -linear sets of the projective line PG ( 1 , q n ) . More recently in [22] and in [5] , new examples of maximum scattered F q -subspaces of V ( 2 , q n ) have been constructed, but the equivalence problem of the corresponding linear sets is left open. Here we show that the F q -linear sets presented in [22] and in [5] , for n = 6 , 8 , are new. Also, for q odd, q ≡ ± 1 , 0 ( mod 5 ) , we present new examples of maximum scattered F q -linear sets in PG ( 1 , q 6 ) , arising from trinomial polynomials, which define new F q -linear MRD-codes of F q 6 × 6 with dimension 12, minimum distance 5 and left idealiser isomorphic to F q 6 . more...
- Published
- 2018
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33. On almost small and almost large super-Vandermonde sets in GF(q)
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Giuseppe Marino, Francesco Mazzocca, Aart Blokhuis, Olga Polverino, Blokhuis, A., Marino, Giuseppe, Mazzocca, F., Polverino, O., Mazzocca, Francesco, Polverino, Olga, Discrete Mathematics, and Discrete Algebra and Geometry more...
- Subjects
Discrete mathematics ,Applied Mathematics ,010102 general mathematics ,Mathematics::History and Overview ,Finite field ,Computer Science Applications1707 Computer Vision and Pattern Recognition ,0102 computer and information sciences ,01 natural sciences ,Vandermonde matrix ,Computer Science Applications ,Combinatorics ,Set (abstract data type) ,TheoryofComputation_MATHEMATICALLOGICANDFORMALLANGUAGES ,010201 computation theory & mathematics ,ComputingMethodologies_SYMBOLICANDALGEBRAICMANIPULATION ,Finite geometry ,Finite fields ,0101 mathematics ,Finite geometry, Finite fields,Vandermonde set ,Vandermonde set ,Mathematics - Abstract
A set (Formula presented.), (Formula presented.) is a super-Vandermonde set if (Formula presented.) for (Formula presented.). We determine the structure of super-Vandermonde sets of size (Formula presented.) (almost small) and size (Formula presented.) (almost large). more...
- Published
- 2017
34. Sufficient conditions to solve two systems of integral equations via fixed point results
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Giuseppe Marino, Badriah A. S. Alamri, Tahair Rasham, Muhammad Arshad, and Abdullah Shoaib
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Closed set ,lcsh:Mathematics ,Applied Mathematics ,010102 general mathematics ,Fixed point ,lcsh:QA1-939 ,Space (mathematics) ,Nonlinear integral equation ,01 natural sciences ,Integral equation ,010101 applied mathematics ,Dislocated b-metric space ,Two families of multivalued mapping ,Application to the system of nonlinear integral equations ,Discrete Mathematics and Combinatorics ,Applied mathematics ,Graph (abstract data type) ,0101 mathematics ,Analysis ,Mathematics - Abstract
The purpose of this paper is to study the solution of two systems of nonlinear integral equations via fixed point results in a complete dislocated b-metric space. Also the notion of graphic contractions on a closed set for two families of graph dominated multivalued mappings is introduced. Our results generalize some previous results in the existing literature. more...
- Published
- 2019
- Full Text
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35. A characterization of linearized polynomials with maximum kernel
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Ferdinando Zullo, Giuseppe Marino, Bence Csajbók, Olga Polverino, Csajbók, Bence, Marino, Giuseppe, Polverino, Olga, and Zullo, Ferdinando
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Algebra and Number Theory ,11T06, 15A04 ,Degree (graph theory) ,Splitting field ,Linear transformation ,Linearized polynomials ,Applied Mathematics ,General Engineering ,Mathematics - Rings and Algebras ,Characterization (mathematics) ,Theoretical Computer Science ,Combinatorics ,Semilinear transformations ,Engineering (all) ,Linearized polynomial ,Rings and Algebras (math.RA) ,Linear transformations, Linearized polynomials, Semilinear transformations ,Linear transformations ,Kernel (statistics) ,FOS: Mathematics ,Mathematics - Combinatorics ,Combinatorics (math.CO) ,Semilinear transformation ,Mathematics - Abstract
We provide sufficient and necessary conditions for the coefficients of a $q$-polynomial $f$ over $\mathbb{F}_{q^n}$ which ensure that the number of distinct roots of $f$ in $\mathbb{F}_{q^n}$ equals the degree of $f$. We say that these polynomials have maximum kernel. As an application we study in detail $q$-polynomials of degree $q^{n-2}$ over $\mathbb{F}_{q^n}$ which have maximum kernel and for $n\leq 6$ we list all $q$-polynomials with maximum kernel. We also obtain information on the splitting field of an arbitrary $q$-polynomial. Analogous results are proved for $q^s$-polynomials as well, where $\gcd(s,n)=1$., Comment: Revised version, final version to appear in Finite Feilds and Their Applications. We added an Appendix with some more details regarding calculations and a proof for Theorem 2.2 to make the paper self-contained more...
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- 2019
36. Projective Paley sets
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Francesco Pavese, Antonio Cossidente, Giuseppe Marino, Cossidente, A., Marino, Giuseppe, and Pavese, F.
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Combinatorics ,Strongly regular graph ,strongly regular graph ,Discrete Mathematics and Combinatorics ,Elliptic quadric ,hyperbolic quadric ,Projective test ,Mathematics - Published
- 2019
37. The covering radius of PGL(3,q)
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Giuseppe Marino, Francesco Pavese, Antonio Cossidente, Cossidente, Antonio, Marino, Giuseppe, and Pavese, Francesco
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Ovoids ,Discrete mathematics ,Group (mathematics) ,Ovoid ,Affine linear group ,Covering radius ,Projective general liner group ,Segre variety ,Veronese variety ,020206 networking & telecommunications ,0102 computer and information sciences ,02 engineering and technology ,Radius ,01 natural sciences ,Theoretical Computer Science ,Combinatorics ,010201 computation theory & mathematics ,0202 electrical engineering, electronic engineering, information engineering ,Covering radiu ,Discrete Mathematics and Combinatorics ,Mathematics - Abstract
In this note, with a purely geometric approach, the covering radius of the group PGL(3, q) is determined. Also, a new proof establishing the covering radii of PGL(2, q) and AGL(1, q) is provided. The research that led to the present paper was partially supported by a grant of the group GNSAGA of INdAM more...
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- 2019
38. Hyperovals arising from a Singer group action on H(3,q2)$\mathcal{H}(3, q^2)$, q even
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Antonio Cossidente, Giuseppe Marino, and Oliver H. King
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Combinatorics ,Action (philosophy) ,010201 computation theory & mathematics ,Group (mathematics) ,010102 general mathematics ,0102 computer and information sciences ,Geometry and Topology ,0101 mathematics ,01 natural sciences ,Mathematics ,Demography - Abstract
The action of a Singer cyclic group of order q 2 + 1 on the Hermitian surface H ( 3 , q 2 ) $\mathcal{H}(3, q^2)$ , q even, is investigated. Infinite families of hyperovals of size 2(q 2 + 1), q even, are then constructed. more...
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- 2016
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39. On the Approximation of Zeros of Non-Self Monotone Operators
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Vittorio Colao, Luigi Muglia, and Giuseppe Marino
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Discrete mathematics ,Control and Optimization ,Iterative method ,010102 general mathematics ,Regular polygon ,Hilbert space ,Inverse ,Fixed point ,Operator theory ,Strongly monotone ,01 natural sciences ,Computer Science Applications ,010101 applied mathematics ,symbols.namesake ,Monotone polygon ,Signal Processing ,symbols ,Applied mathematics ,0101 mathematics ,Analysis ,Mathematics - Abstract
In this article, we study the approximation of common zeros of non-self inverse strongly monotone operators defined on a closed convex subset C of a Hilbert space H. For a non-self family of operators, we introduce an iterative algorithm without relying on projections. Approximation of common fixed points for finite families of non-self strict pseudo-contractions in the sense of Browder-Petryshyn is also obtained. The novelty of our algorithm is that the coefficients are not given a priori and no assumptions are made on them, but they are constructed step by step in a natural way. more...
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- 2016
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40. On the approximation of fixed points of non-self strict pseudocontractions
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Giuseppe Marino, Nawab Hussain, and Vittorio Colao
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Discrete mathematics ,Algebra and Number Theory ,Applied Mathematics ,010102 general mathematics ,Fixed point ,Lambda ,01 natural sciences ,010101 applied mathematics ,Computational Mathematics ,Geometry and Topology ,0101 mathematics ,Convex function ,Analysis ,Mathematics - Abstract
Let H be a Hilbert space and let C be a closed, convex and nonempty subset of H. If \(T:C\rightarrow H\) is a non-self and k-strict pseudocontractive mapping, we can define a map \(v:C\rightarrow \mathbb {R}\) by \(\, v(x):=\inf \{\lambda \ge 0:\lambda x+(1-\lambda )Tx\in C\}.\) Then, for a fixed \(x_{0}\in C\) and for \(\alpha _{0}:=\max \{k,v(x_{0})\},\) we define the Krasnoselskii–Mann algorithm \(x_{n+1}=\alpha _{n}x_{n}+(1-\alpha _{n})Tx_{n},\) where \(\alpha _{n+1}=\max \{\alpha _{n},v(x_{n+1})\}.\) So, here the coefficients \(\alpha _{n}\) are not chosen a priori, but built step by step. We prove both weak and strong convergence results when C is a strictly convex set and T is an inward mapping. more...
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- 2016
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41. MRD codes with maximum idealizers
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Bence Csajbók, Yue Zhou, Olga Polverino, Giuseppe Marino, Csajbok, B., Marino, G., Polverino, O., and Zhou, Y.
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Left and right ,Discrete mathematics ,Code (set theory) ,Idealizer ,Gabidulin code ,94B05, 11T06, 15A04 ,Algebraic curve, Idealizer, Gabidulin code, linearized polynomial, Moore matrix, MRD code ,Moore matrix ,Theoretical Computer Science ,Combinatorics ,Finite field ,linearized polynomial ,MRD code ,Algebraic curve ,FOS: Mathematics ,Discrete Mathematics and Combinatorics ,Mathematics - Combinatorics ,Combinatorics (math.CO) ,Idealizer, Gabidulin code ,Mathematics ,Computer Science::Information Theory - Abstract
Left and right idealizers are important invariants of linear rank-distance codes. In the case of maximum rank-distance (MRD for short) codes in $\mathbb{F}_q^{n\times n}$ the idealizers have been proved to be isomorphic to finite fields of size at most $q^n$. Up to now, the only known MRD codes with maximum left and right idealizers are generalized Gabidulin codes, which were first constructed in 1978 by Delsarte and later generalized by Kshevetskiy and Gabidulin in 2005. In this paper we classify MRD codes in $\mathbb{F}_q^{n\times n}$ for $n\leq 9$ with maximum left and right idealizers and connect them to Moore-type matrices. Apart from generalized Gabidulin codes, it turns out that there is a further family of rank-distance codes providing MRD ones with maximum idealizers for $n=7$, $q$ odd and for $n=8$, $q\equiv 1 \pmod 3$. These codes are not equivalent to any previously known MRD code. Moreover, we show that this family of rank-distance codes does not provide any further examples for $n\geq 9$., Reviewers' comments implemented, we changed the title more...
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- 2018
42. A new family of MRD-codes
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Giuseppe Marino, Bence Csajbók, Corrado Zanella, Olga Polverino, Csajbók, Bence, Marino, Giuseppe, Polverino, Olga, and Zanella, Corrado
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Scattered subspace ,Numerical Analysis ,Algebra and Number Theory ,010102 general mathematics ,Linear set ,MRD-code ,Geometry and Topology ,Discrete Mathematics and Combinatorics ,0102 computer and information sciences ,Linear set, MRD-code, Scattered subspace ,Type (model theory) ,01 natural sciences ,Combinatorics ,010201 computation theory & mathematics ,Yield (chemistry) ,FOS: Mathematics ,Mathematics - Combinatorics ,51E20, 05B25, 51E22 ,Combinatorics (math.CO) ,0101 mathematics ,Numerical Analysi ,Mathematics - Abstract
We introduce a family of linear sets of PG ( 1 , q 2 n ) arising from maximum scattered linear sets of pseudoregulus type of PG ( 3 , q n ) . For n = 3 , 4 and for certain values of the parameters we show that these linear sets of PG ( 1 , q 2 n ) are maximum scattered and they yield new MRD-codes with parameters ( 6 , 6 , q ; 5 ) for q > 2 and with parameters ( 8 , 8 , q ; 7 ) for q odd. more...
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- 2018
43. On symplectic semifield spreads of PG(5,q 2), q odd
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Giuseppe Marino, Valentina Pepe, Marino, Giuseppe, and Pepe, Valentina
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Pure mathematics ,General Mathematics ,Commutative semifeld ,Symplectic semifeld spread ,Veronese variety ,Mathematics (all) ,Applied Mathematics ,010102 general mathematics ,0102 computer and information sciences ,01 natural sciences ,symplectic semifield spread ,010201 computation theory & mathematics ,0101 mathematics ,Commutative semifield ,Semifield ,Symplectic geometry ,Mathematics - Abstract
We prove that there exist exactly three non-equivalent symplectic semifield spreads of PG ( 5 , q 2 ) {\operatorname{PG}(5,q^{2})} , for q 2 > 2 ⋅ 3 8 {q^{2}>2\cdot 3^{8}} odd, whose associated semifield has center containing 𝔽 q {\mathbb{F}_{q}} . Equivalently, we classify, up to isotopy, commutative semifields of order q 6 {q^{6}} , for q 2 > 2 ⋅ 3 8 {q^{2}>2\cdot 3^{8}} odd, with middle nucleus containing 𝔽 q 2 {\mathbb{F}_{q^{2}}} and center containing 𝔽 q {\mathbb{F}_{q}} . more...
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- 2018
44. Matrix approaches to approximate solutions of variational inequalities in Hilbert spaces
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Giuseppe Marino, Luigi Muglia, Hong-Kun Xu, and Filomena Cianciaruso
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Control and Optimization ,Iterative method ,Applied Mathematics ,010102 general mathematics ,Ergodicity ,Mathematical analysis ,Hilbert space ,Management Science and Operations Research ,01 natural sciences ,Regularization (mathematics) ,Toeplitz matrix ,010101 applied mathematics ,Matrix (mathematics) ,symbols.namesake ,Variational inequality ,symbols ,Ergodic theory ,Applied mathematics ,0101 mathematics ,Mathematics - Abstract
A matrix approach to approximating solutions of variational inequalities in Hilbert spaces is introduced. This approach uses two matrices: one for iteration process and the other for regularization. Ergodicity and convergence (both weak and strong) are studied. Our methods combine new or well-known iterative methods (such as the original Mann’s method) with regularized processes involved regular matrices in the sense of Toeplitz. more...
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- 2015
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45. On the strong convergence of a general-type Krasnosel’skii–Mann’s algorithm depending on the coefficients
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Luigi Muglia, Newab Hussain, Giuseppe Marino, and Afrah A. N. Abdou
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Discrete mathematics ,021103 operations research ,Iterative method ,Applied Mathematics ,Operator (physics) ,0211 other engineering and technologies ,Hilbert space ,02 engineering and technology ,Type (model theory) ,Strongly monotone ,01 natural sciences ,010101 applied mathematics ,symbols.namesake ,Modeling and Simulation ,Scheme (mathematics) ,Variational inequality ,Convergence (routing) ,symbols ,Geometry and Topology ,0101 mathematics ,Mathematics - Abstract
Let H be a Hilbert space, (Wn)nN a suitable family of map- pings, S a nonexpansive mapping and D a strongly monotone operator. We are interested in the strong convergence of the general scheme
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- 2015
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46. Non-linear maximum rank distance codes
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Giuseppe Marino, Francesco Pavese, Antonio Cossidente, Cossidente, Antonio, Marino, Giuseppe, and Pavese, Francesco
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Rank (linear algebra) ,0102 computer and information sciences ,02 engineering and technology ,Veronese variety ,01 natural sciences ,Constant rank distance code ,Maximum rank distance code ,Segre variety ,Singer cyclic group ,Subspace codes ,Combinatorics ,Mathematics::Algebraic Geometry ,0202 electrical engineering, electronic engineering, information engineering ,Segre variety, Veronese variety, Maximum rank distance code, Constant rank distance code, Subspace codes, Singer cyclic group ,Mathematics ,Mathematics::Commutative Algebra ,Applied Mathematics ,Computer Science Applications1707 Computer Vision and Pattern Recognition ,020206 networking & telecommunications ,Linear code ,Computer Science Applications ,Nonlinear system ,Maximum rank ,010201 computation theory & mathematics ,Optimal constant ,Subspace code - Abstract
By exploring some geometry of Segre varieties and Veronese varieties, new families of non linear maximum rank distance codes and optimal constant rank codes are provided.
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- 2015
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47. A natural extension of the Young partition lattice
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Cinzia Bisi, Giampiero Chiaselotti, Paolo A. Oliverio, and Giuseppe Marino
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Combinatorics ,integer partitions ,Graded lattices ,sand piles models ,Young diagrams ,Socio-culturale ,Partition lattice ,Geometry and Topology ,Extension (predicate logic) ,Graded lattices, integer partitions, Young diagrams, sand piles models ,Natural (archaeology) ,Mathematics - Abstract
Recently Andrews introduced the concept of signed partition: a signed partition is a finite sequence of integers ak, . . . , a1, a−1, . . . , a−l such that ak ≥ ... ≥ a1 > 0 > a−1 ≥ ... ≥ a−l. So far the signed partitions have been studied from an arithmetical point of view. In this paper we first generalize the concept of signed partition and we next use such a generalization to introduce a partial order on the set of all the signed partitions. Furthermore, we show that this order has many remarkable properties and that it generalizes the classical order on the Young lattice. more...
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- 2015
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48. Function Spaces, Fixed Points, Approximations, and Applications
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Filomena Cianciaruso, Giuseppe Marino, Nawab Hussain, and Enrique Llorens Fuster
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Article Subject ,Fixed-point iteration ,Function space ,lcsh:Mathematics ,Applied mathematics ,Fixed point ,lcsh:QA1-939 ,Fixed-point property ,Analysis ,Mathematics - Published
- 2017
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49. On maximal cliques of polar graphs
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Giuseppe Marino, Antonio Cossidente, Francesco Pavese, Cossidente, Antonio, Marino, Giuseppe, Pavese, Francesco, Cossidente, A., Marino, G., and Pavese, F
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Discrete mathematics ,Strongly regular graph ,Maximal clique ,Hermitian surface ,Hyperbolic quadric ,Elliptic quadric ,Clique-sum ,Algebra and Number Theory ,Symmetric graph ,Applied Mathematics ,General Engineering ,Distance-regular graph ,Simplex graph ,Theoretical Computer Science ,Combinatorics ,Elliptic quadric, Hermitian surfaces, Hyperbolic quadric, Maximal clique, Strongly regular graphs ,Circulant graph ,Engineering (all) ,Trivially perfect graph ,K-tree ,Turán graph ,Mathematics - Abstract
The maximal cliques of the graph NU ( 4 , q 2 ) related to the Hermitian surface of PG ( 3 , q 2 ) and of the graph NO ± ( 2 n + 2 , q ) , q even, n ≥ 1 , are classified.
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- 2017
50. The Generalized Translation Dual of a Semifield
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Olga Polverino, Rocco Trombetti, Giuseppe Marino, Guglielmo Lunardon, Lunardon, G., Marino, G., Polverino, O., Trombetti, R., Lunardon, Guglielmo, and Trombetti, Rocco
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Discrete mathematics ,Rank (linear algebra) ,010102 general mathematics ,Dimension (graph theory) ,semifield ,0102 computer and information sciences ,Disjoint sets ,Link (geometry) ,linear set ,01 natural sciences ,Segre variety ,Left nucleus ,Combinatorics ,Secant variety ,010201 computation theory & mathematics ,semifield, linear set, Segre variety ,Discrete Mathematics and Combinatorics ,0101 mathematics ,Variety (universal algebra) ,Semifield ,Mathematics - Abstract
In this paper, elaborating on the link between semifields of dimension n over their left nucleus and $${\mathbb{F}s}$$ -linear sets of rank en disjoint from the secant variety $${\Omega(\mathcal{S}_{n,n})}$$ of the Segre variety $${\mathcal{S}_{n,n}}$$ of $${PG(n^2-1, q), q=s^e}$$ , we extend some operations on semifield whose definition relies on dualising the relevant linear set. more...
- Published
- 2017
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