23 results
Search Results
2. Generalized split null point of sum of monotone operators in Hilbert spaces
- Author
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H. A. Abass, Olalwale K. Oyewole, Ojen Kumar Narain, Akindele Adebayo Mebawondu, and Kazeem Olalekan Aremu
- Subjects
47h09 ,Pure mathematics ,fixed point problem ,47j25 ,General Mathematics ,47j05 ,Hilbert space ,47h06 ,inertial iterative scheme ,symbols.namesake ,Monotone polygon ,firmly nonexpansive ,symbols ,generalized split monotone variational inclusion ,QA1-939 ,Null point ,Mathematics - Abstract
In this paper, we introduce a new type of a generalized split monotone variational inclusion (GSMVI) problem in the framework of real Hilbert spaces. By incorporating an inertial extrapolation method and an Halpern iterative technique, we establish a strong convergence result for approximating a solution of GSMVI and fixed point problems of certain nonlinear mappings in the framework of real Hilbert spaces. Many existing results are derived as corollaries to our main result. Furthermore, we present a numerical example to support our main result and propose an open problem for interested researchers in this area. The result obtained in this paper improves and generalizes many existing results in the literature.
- Published
- 2021
3. Some results on generalized finite operators and range kernel orthogonality in Hilbert spaces
- Author
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Hadia Messaoudene, Asma Alharbi, and Nadia Mesbah
- Subjects
Pure mathematics ,General Mathematics ,Hilbert space ,numerical range ,class ℛ¯1 ,symbols.namesake ,Range (mathematics) ,Orthogonality ,47a12 ,orthogonality ,Kernel (statistics) ,symbols ,47a30 ,QA1-939 ,finite operator ,47b47 ,Mathematics - Abstract
Let ℋ {\mathcal{ {\mathcal H} }} be a complex Hilbert space and ℬ ( ℋ ) {\mathcal{ {\mathcal B} }}\left({\mathcal{ {\mathcal H} }}) denotes the algebra of all bounded linear operators acting on ℋ {\mathcal{ {\mathcal H} }} . In this paper, we present some new pairs of generalized finite operators. More precisely, new pairs of operators ( A , B ) ∈ ℬ ( ℋ ) × ℬ ( ℋ ) \left(A,B)\in {\mathcal{ {\mathcal B} }}\left({\mathcal{ {\mathcal H} }})\times {\mathcal{ {\mathcal B} }}\left({\mathcal{ {\mathcal H} }}) satisfying: ∥ A X − X B − I ∥ ≥ 1 , for all X ∈ ℬ ( ℋ ) . \parallel AX-XB-I\parallel \ge 1,\hspace{1.0em}\hspace{0.1em}\text{for all}\hspace{0.1em}\hspace{0.33em}X\in {\mathcal{ {\mathcal B} }}\left({\mathcal{ {\mathcal H} }}). An example under which the class of such operators is not invariant under similarity orbit is given. Range kernel orthogonality of generalized derivation is also studied.
- Published
- 2021
4. Range-Kernel orthogonality and elementary operators on certain Banach spaces
- Author
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Ahmed Bachir, Khalid Ouarghi, Abdelkader Segres, and Nawal Ali Sayyaf
- Subjects
trace class operators ,Pure mathematics ,schatten p-classes ,Nuclear operator ,General Mathematics ,Banach space ,47b10 ,Kernel (algebra) ,Range (mathematics) ,46b20 ,47b20 ,Orthogonality ,range-kernel orthogonality ,47a30 ,QA1-939 ,elementary operator ,47b47 ,Mathematics - Abstract
The characterization of the points in C p : 1 ≤ p < ∞ ( ℋ ) {C}_{p{:}_{1\le p\lt \infty }}\left({\mathcal{ {\mathcal H} }}) , the Von Neuman-Schatten p-classes, that are orthogonal to the range of elementary operators has been done for certain kinds of elementary operators. In this paper, we shall study this problem of characterization on an abstract reflexive, smooth and strictly convex Banach space for arbitrary operator. As an application, we consider other kinds of elementary operators defined on the spaces C p : 1 ≤ p < ∞ ( ℋ ) {C}_{p{:}_{1\le p\lt \infty }}\left({\mathcal{ {\mathcal H} }}) , and finally, we give a counterexample to Mecheri’s result given in this context.
- Published
- 2021
5. On some fixed point theorems for multivalued F-contractions in partial metric spaces
- Author
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Santosh Kumar and Sholastica Luambano
- Subjects
Pure mathematics ,General Mathematics ,partial metric spaces ,010102 general mathematics ,Fixed-point theorem ,Mathematics::General Topology ,01 natural sciences ,fixed point theorems ,010101 applied mathematics ,Metric space ,54h25 ,multivalued f-contraction mappings ,ComputingMethodologies_DOCUMENTANDTEXTPROCESSING ,QA1-939 ,0101 mathematics ,GeneralLiterature_REFERENCE(e.g.,dictionaries,encyclopedias,glossaries) ,47h10 ,Mathematics - Abstract
Altun et al. explored the existence of fixed points for multivalued F F -contractions and proved some fixed point theorems in complete metric spaces. This paper extended the results of Altun et al. in partial metric spaces and proved fixed point theorems for multivalued F F -contraction mappings. Some illustrative examples are provided to support our results. Moreover, an application for the existence of a solution of an integral equation is also enunciated, showing the materiality of the obtained results.
- Published
- 2021
6. On q-analogue of Janowski-type starlike functions with respect to symmetric points
- Author
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Bakhtiar Ahmad, Muhammad Zubair, Raees Khan, Muhammad Ghaffar Khan, and Zabidin Salleh
- Subjects
Pure mathematics ,starlike functions ,General Mathematics ,010102 general mathematics ,janowski functions ,02 engineering and technology ,30c45 ,Type (model theory) ,30c50 ,01 natural sciences ,0202 electrical engineering, electronic engineering, information engineering ,holomorphic functions ,QA1-939 ,020201 artificial intelligence & image processing ,0101 mathematics ,subordinations ,Mathematics - Abstract
The main objective of the present paper is to define a class of q q -starlike functions with respect to symmetric points in circular domain. Some interesting results of these functions have been evaluated in this article. The sufficiency criteria in the form of convolutions are evaluated. Furthermore, other geometric properties such as coefficient bounds, distortion theorem, closure theorem and extreme point theorem are also obtained for these newly defined functions.
- Published
- 2021
7. Hyers-Ulam stability of quadratic forms in 2-normed spaces
- Author
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Jae-Hyeong Bae and Won-Gil Park
- Subjects
Pure mathematics ,Mathematics::Functional Analysis ,Mathematics::Operator Algebras ,General Mathematics ,linear 2-normed space ,hyers-ulam stability ,010102 general mathematics ,Stability (learning theory) ,Mathematics::Classical Analysis and ODEs ,39b52 ,01 natural sciences ,quadratic form ,010101 applied mathematics ,Nonlinear Sciences::Chaotic Dynamics ,Quadratic form ,39b72 ,QA1-939 ,0101 mathematics ,Nonlinear Sciences::Pattern Formation and Solitons ,Mathematics - Abstract
In this paper, we obtain Hyers-Ulam stability of the functional equations f (x + y, z + w) + f (x − y, z − w) = 2f (x, z) + 2f (y, w), f (x + y, z − w) + f (x − y, z + w) = 2f (x, z) + 2f (y, w) and f (x + y, z − w) + f (x − y, z + w) = 2f (x, z) − 2f (y, w) in 2-Banach spaces. The quadratic forms ax 2 + bxy + cy 2, ax 2 + by 2 and axy are solutions of the above functional equations, respectively.
- Published
- 2019
8. Characterizations of compact operators on ℓp−type fractional sets of sequences
- Author
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Faruk Özger
- Subjects
Pure mathematics ,General Mathematics ,010102 general mathematics ,compact operator ,02 engineering and technology ,Type (model theory) ,Compact operator ,01 natural sciences ,Fractional operator ,fractional operator ,operator norm ,gamma function ,0202 electrical engineering, electronic engineering, information engineering ,QA1-939 ,020201 artificial intelligence & image processing ,0101 mathematics ,Gamma function ,46b45 ,Operator norm ,hausdorff measure of noncompactness ,Mathematics ,47b37 - Abstract
Among the sets of sequences studied, difference sets of sequences are probably the most common type of sets. This paper considers some ℓp−type fractional difference sets via the gamma function. Although, we characterize compactness conditions on those sets using the main key of Hausdorff measure of noncompactness, we can only obtain sufficient conditions when the final space is ℓ∞. However, we use some recent results to exactly characterize the classes of compact matrix operators when the final space is the set of bounded sequences.
- Published
- 2019
9. Approximation properties of Kantorovich type q-Balázs-Szabados operators
- Author
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Esma Yıldız Özkan
- Subjects
Pure mathematics ,General Mathematics ,010102 general mathematics ,balázs-szabados operators ,Type (model theory) ,01 natural sciences ,010101 applied mathematics ,Rate of convergence ,peetre’s k-functional ,QA1-939 ,0101 mathematics ,q-calculus ,41a25 ,41a36 ,Mathematics ,rate of convergence ,41a35 - Abstract
In this paper, we introduce a new kind of q-Balázs-Szabados-Kantorovich operators called q-BSK operators. We give a weighted statistical approximation theorem and the rate of convergence of the q-BSK operators. Also, we investigate the local approximation results. Further, we give some comparisons associated with the convergence of q-BSK operators.
- Published
- 2019
10. Approximate property of a functional equation with a general involution
- Author
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Won-Gil Park and Jae-Hyeong Bae
- Subjects
Involution (mathematics) ,Pure mathematics ,Banach space ,General Mathematics ,lcsh:Mathematics ,involution ,lcsh:QA1-939 ,approximation ,Mathematics - Abstract
In this paper, we prove the Hyers-Ulam stability of the functional equation f(x + y, z + w) + f(x + σ(y),z + τ(w)) = 2f(x, z) + 2f(y, w), where σ, τ are involutions.
- Published
- 2018
11. Certain Laplace transforms of convolution type integrals involving product of two special pFp functions
- Author
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Rakesh K. Parmar, Arjun K. Rathie, and Gradimir V. Milovanović
- Subjects
Pure mathematics ,Convolution type integrals ,Laplace transform ,33C90 ,General Mathematics ,010103 numerical & computational mathematics ,02 engineering and technology ,Kummer’s summation theorem ,Type (model theory) ,01 natural sciences ,Watson’s summation theorem ,Convolution ,Dougall’s theorem ,0202 electrical engineering, electronic engineering, information engineering ,Gauss’s summation theorem ,Gauss’s second summation theorem ,0101 mathematics ,Dixon’s summation theorem ,Primary 33C20 ,Mathematics ,lcsh:Mathematics ,lcsh:QA1-939 ,Secondary 33C05 ,Product (mathematics) ,Bailey’s summation theorem ,020201 artificial intelligence & image processing ,Whipple’s first and second summation theorems - Abstract
Recently the authors obtained several Laplace transforms of convolution type integrals involving Kummer’s function 1F1 [Appl. Anal. Discrete Math., 2018, 12(1), 257-272]. In this paper, the authors aim at presenting several new and interesting Laplace transforms of convolution type integrals involving product of two special generalized hypergeometric functions pFp by employing classical summation theorems for the series 2F1, 3F2, 4F3 and 5F4 available in the literature.
- Published
- 2018
12. On generalized Baskakov-Durrmeyer-Stancu type operators
- Author
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Purshottam Narain Agrawal, Zoltán Finta, and Angamuthu Sathish Kumar
- Subjects
Pure mathematics ,General Mathematics ,Microlocal analysis ,Spectral theorem ,Type (model theory) ,01 natural sciences ,Fourier integral operator ,Baskakov-Durrmeyer-Stancu operators ,Lipschitz type space ,A-statistical convergence ,0101 mathematics ,41A25 ,Mathematics ,lcsh:Mathematics ,010102 general mathematics ,Operator theory ,lcsh:QA1-939 ,010101 applied mathematics ,26A15 ,26A16 ,Baskakov operator ,Rate of convergence ,modulus of smoothness ,41A36 ,Operator norm ,rate of convergence - Abstract
In this paper, we study some local approximation properties of generalized Baskakov-Durrmeyer-Stancu operators. First, we establish a recurrence relation for the central moments of these operators, then we obtain a local direct result in terms of the second order modulus of smoothness. Further, we study the rate of convergence in Lipschitz type space and the weighted approximation properties in terms of the modulus of continuity, respectively. Finally, we investigate the statistical approximation property of the new operators with the aid of a Korovkin type statistical approximation theorem.
- Published
- 2017
13. Painlevé Equation PII and Strongly Normal Extensions
- Author
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Sofiane El-Hadi Miri
- Subjects
strongly normal extensions ,Pure mathematics ,Painlevé equation PII ,General Mathematics ,lcsh:Mathematics ,Mathematical analysis ,differential algebra ,lcsh:QA1-939 ,Mathematics - Abstract
The aim of this paper is to show that if F is a differential field and y is a PII transcendent such that tr.deg.F 〈y〉 = 2, then every constant in F〈y〉 is in F. We also show that in this case, F〈y〉 is not contained in any strongly normal extension.
- Published
- 2016
14. More on Ostrowski Type Inequalities for some S-Convex Functions in the Second Sense
- Author
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Zeng Liu
- Subjects
Hölder's inequality ,convex function ,Pure mathematics ,Inequality ,General Mathematics ,media_common.quotation_subject ,Hölder inequality ,lcsh:Mathematics ,010102 general mathematics ,Ostrowski type inequality ,Sense (electronics) ,Type (model theory) ,lcsh:QA1-939 ,01 natural sciences ,010101 applied mathematics ,s-convex function ,0101 mathematics ,Convex function ,media_common ,Mathematics - Abstract
Some Ostrowski type inequalities for functions whose second derivatives in absolute value at certain powers are s-convex in the second sense are established. Two mistakes in a recently published paper are pointed out and corrected.
- Published
- 2016
15. Common Fixed Point Theorems for Mappings under (CLRS)-Property in Partial Metric Spaces
- Author
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Mohammad Imdad, K. V. Siva Parvathi, and K. P. R. Rao
- Subjects
Discrete mathematics ,Pure mathematics ,Property (philosophy) ,General Mathematics ,w-compatible mappings ,lcsh:Mathematics ,010102 general mathematics ,lcsh:QA1-939 ,01 natural sciences ,(CLRS)-property ,partial metric ,010101 applied mathematics ,Metric space ,Common fixed point ,0101 mathematics ,Mathematics - Abstract
In this paper, we introduce the concept of (CLRS)-property for mappings F : X × X→X and S : X → X (wherein X stands for a partial metric space) and utilize the same to prove two common fixed point theorems for two pairs of mappings in partial metric spaces. We also furnish two examples to illustrate our main theorems.
- Published
- 2016
16. On The K-Pseudo Symmetric and Ordinary Differentiation
- Author
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E. Łazarow and M. Turowska
- Subjects
Pure mathematics ,General Mathematics ,σ-porous set ,lcsh:Mathematics ,ordinary derivative ,lcsh:QA1-939 ,k-pseudo symmetric derivative ,Mathematics - Abstract
In 1972, S. Valenti introduced the definition of k-pseudo symmetric derivative and has shown that the set of all points of a continuous function, at which there exists a finite k-pseudo symmetric derivative but the finite ordinary derivative does not exist, is of Lebesgue measure zero. In 1993, L. Zajícek has shown that for a continuous function f, the set of all points, at which f is symmetrically differentiable but no differentiable, is σ-(1 - ε) symmetrically porous for every ε > 0. The question arises: can we transferred the Zajícek’s result to the case of the k-pseudo symmetric derivative?In this paper, we shall show that for each 0 < ε < 1 the set of all points of a continuous function, at which there exists a finite k-pseudo symmetric derivative but the finite ordinary derivative does not exist, is σ-(1 - ε)-porous.
- Published
- 2016
17. Intuitionistic fuzzy almost Cauchy–Jensen mappings
- Author
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M. E. Gordji and Sadegh Abbaszadeh
- Subjects
Hyers–Ulam stability ,46S40 ,Pure mathematics ,Cauchy–Jensen mapping ,General Mathematics ,lcsh:Mathematics ,47S40 ,39B52 ,Cauchy distribution ,Intuitionistic fuzzy ,010103 numerical & computational mathematics ,lcsh:QA1-939 ,01 natural sciences ,010305 fluids & plasmas ,34K36 ,0103 physical sciences ,39B82 ,0101 mathematics ,26E50 ,intuitionistic fuzzy Banach space ,Mathematics - Abstract
In this paper, we first investigate the Hyers–Ulam stability of the generalized Cauchy–Jensen functional equation of p-variable f(∑i=1paixi)=∑i=1paif(xi)$f\left(\sum\nolimits_{i = 1}^p {a_i x_i } \right) = \sum\nolimits_{i = 1}^p {a_i f(x_i )}$ in an intuitionistic fuzzy Banach space. Then, we conclude the results for Cauchy–Jensen functional equation of p-variable f(x1+⋯+xpp)=1p(f(x1)+⋯+f(xp))$f\left( {{\textstyle{{x_1 + \cdots + x_p } \over p}}} \right) = {1 \over p}(f(x_1 ) + \cdots + f(x_p ))$ . Next, we discuss the intuitionistic fuzzy continuity of Cauchy–Jensen mappings.
- Published
- 2016
18. Free Algebras Over a Poset in Varieties of Łukasiewicz–Moisil Algebras
- Author
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C. Gallardo and A. Figallo Orellano
- Subjects
Pure mathematics ,Jordan algebra ,Mathematics::Combinatorics ,General Mathematics ,lcsh:Mathematics ,Subalgebra ,Non-associative algebra ,MV-algebra ,Łukasiewicz-Moisil algebras ,lcsh:QA1-939 ,Cayley–Dickson construction ,algebras ,Interior algebra ,Division algebra ,free algebras over a poset ,Generalized Kac–Moody algebra ,Mathematics - Abstract
A general construction of the free algebra over a poset in varieties finitely generated is given in [8]. In this paper, we apply this to the varieties of Łukasiewicz-Moisil algebras, giving a detailed description of the free algebra over a finite poset (X, ≤) , Freen((X, ≤)). As a consequence of this description, the cardinality of Freen((X, ≤)). is computed for special posets.
- Published
- 2015
19. A Generalized Common Fixed Point Theorem under an Implicit Relation
- Author
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D. Surekha and T. Phaneendra
- Subjects
Discrete mathematics ,Pure mathematics ,orbitally complete metric space ,implicit-type relation ,Relation (database) ,General Mathematics ,lcsh:Mathematics ,common fixed point ,weakly compatible maps ,lcsh:QA1-939 ,property E.A ,Common fixed point ,Common fixed point theorem ,Mathematics - Abstract
An extended generalization of recent result of Kikina and Kikina (2011) has been established through the notions of weak compatibility and the property E.A., under an implicit-type relation and restricted orbital completeness of the space. The result of this paper also extends and generalizes that of Imdad and Ali (2007).
- Published
- 2015
20. On Derivations of Operator Algebras with Involution
- Author
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Nejc Širovnik and Joso Vukman
- Subjects
Discrete mathematics ,Pure mathematics ,Banach space ,Jordan derivation ,General Mathematics ,lcsh:Mathematics ,Semiprime ring ,Hilbert space ,derivation ,lcsh:QA1-939 ,Operator space ,semiprime ring ,ring ,Linear map ,prime ring ,standard operator algebra ,symbols.namesake ,Operator algebra ,and phrases ring ,Bounded function ,Prime ring ,symbols ,Mathematics - Abstract
The purpose of this paper is to prove the following result. Let X be a complex Hilbert space, let L(X) be an algebra of all bounded linear operators on X and let A(X) ⊂ L(X) be a standard operator algebra, which is closed under the adjoint operation. Suppose there exists a linear mapping D : A(X) → L(X) satisfying the relation 2D(AA*A) = D(AA*)A + AA*D(A) + D(A)A*A + AD(A*A) for all A ∈ A(X). In this case, D is of the form D(A) = [A,B] for all A ∈ A(X) and some fixed B ∈ L(X), which means that D is a derivation.
- Published
- 2014
21. New Geometric Interpretation of Quaternionic Fueter Functions
- Author
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Wiesław Królikowski
- Subjects
Fueter regular function (quaternionic analysis) ,Pure mathematics ,Mathematics::Complex Variables ,General Mathematics ,lcsh:Mathematics ,Mathematical analysis ,and phrases fundamental 2-form ,Kähler manifold ,lcsh:QA1-939 ,Quaternionic analysis ,Interpretation (model theory) ,almost Kähler manifold (complex analysis) ,Mathematics::Differential Geometry ,Mathematics - Abstract
Introduction It is interesting that using the properties of quaternionic regular functions in the sense of Fueter, one can obtain the significant results in complex analysis (see, e.g. [1], [3]). There are many amazing relations between quaternionic functions and some objects of complex analysis. This paper is devoted to show one of them, namely that there is a correspondence between quaternionic regular functions in the sense of Fueter and fundamental 2-forms on a 4-dimensional almost Kahler manifold.
- Published
- 2014
22. Radical Transversal Lightlike Submanifolds of Indefinite Para-Sasakian Manifolds
- Author
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S. S. Shukla and Akhilesh Yadav
- Subjects
Pure mathematics ,degenerate metric ,screen distribution ,Mathematics::Complex Variables ,General Mathematics ,lcsh:Mathematics ,Mathematical analysis ,Radial distribution ,lcsh:QA1-939 ,and phrases semi-Riemannian manifold ,General Relativity and Quantum Cosmology ,Transversal (combinatorics) ,lightlike transversal vector bundle ,Gauss and Weingarten formulae ,radical distribution ,Mathematics::Differential Geometry ,screen transversal vector bundle ,Nuclear Experiment ,Mathematics::Symplectic Geometry ,Mathematics - Abstract
In this paper, we study radical transversal lightlike submanifolds and screen slant radical transversal lightlike submanifolds of indefinite para-Sasakian manifolds giving some non-trivial examples of these submanifolds. Integrability conditions of distributions D and RadTM on radical transversal lightlike submanifolds and screen slant radical transversal lightlike submanifolds of indefinite para-Sasakian manifolds, have been obtained. We also study totally contact umbilical radical transversal lightlike submanifolds of indefinite para-Sasakian manifolds.
- Published
- 2014
23. Generalizations of Opial-Type Inequalities in Several Independent Variables
- Author
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Maja Andrić, Ana Barbir, Gholam Roqia, and Josip Pečarić
- Subjects
Pure mathematics ,Variables ,Willett’s inequality ,Inequality ,General Mathematics ,media_common.quotation_subject ,lcsh:Mathematics ,Opial-type inequalities ,Willett's inequality ,Rozanova's inequality ,several independent variables ,Type (model theory) ,Rozanova’s inequality ,lcsh:QA1-939 ,Calculus ,and phrases Opial-type inequalities ,media_common ,Mathematics - Abstract
In this paper, we consider Willett’s and Rozanova’s generalizations of Opial’s inequality and extend them to inequalities in several independent variables. Also, we present some new Opial-type inequalities in several independent variables.
- Published
- 2014
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