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132 results on '"Al Rawashdeh, Ahmed"'

3. Generalized Dobrushin Ergodicity Coefficient and Ergodicities of Non-homogeneous Markov Chains

Author

Mukhamedov, Farrukh and Al-Rawashdeh, Ahmed

Subjects
Mathematics - Functional Analysis, Mathematics - Dynamical Systems, Mathematics - Operator Algebras, Mathematics - Probability, 47A35, 60J10, 28D05
Abstract

In our earlier paper, a generalized Dobrushin ergodicity coefficient of Markov operators (acting on abstract state spaces) with respect to a projection $P$, has been introduced and studied. It turned out that the introduced coefficient was more effective than the usual ergodicity coefficient. In the present work, by means of a left consistent Markov projections and the generalized Dobrushin's ergodicity coefficient, we investigate uniform and weak $P$-ergodicities of non-homogeneous discrete Markov chains (NDMC) on abstract state spaces. It is easy to show that uniform $P$-ergodicity implies a weak one, but in general the reverse is not true. Therefore, some conditions are provided together with weak $P$-ergodicity of NDMC which imply its uniform $P$-ergodicity. Furthermore, necessary and sufficient conditions are found by means of the Doeblin's condition for the weak $P$-ergodicity of NDMC. The weak $P$-ergodicity is also investigated in terms of perturbations. Several perturbative results are obtained which allow us to produce nontrivial examples of uniform and weak $P$-ergodic NDMC. Moreover, some category results are also obtained. We stress that all obtained results have potential applications in the classical and non-commutative probabilities., Comment: 29 pages. arXiv admin note: text overlap with arXiv:2001.06266

Published
2020

4. Generalized Dobrushin Ergodicity Coefficient and Uniform Ergodicities of Markov Operators

Author

Mukhamedov, Farrukh and Al-Rawashdeh, Ahmed

Subjects
Mathematics - Functional Analysis, Mathematics - Operator Algebras, Mathematics - Probability, 47A35, 60J10, 28D05
Abstract

In this paper the stability and the perturbation bounds of Markov operators acting on abstract state spaces are investigated. Here, an abstract state space is an ordered Banach space where the norm has an additivity property on the cone of positive elements. We basically study uniform ergodic properties of Markov operators by means of so-called a generalized Dobrushin's ergodicity coefficient. This allows us to get several convergence results with rates. Some results on quasi-compactness of Markov operators are proved in terms of the ergodicity coefficient. Furthermore, a characterization of uniformly $P$-ergodic Markov operators is given which enable us to construct plenty examples of such types of operators. The uniform mean ergodicity of Markov operators is established in terms of the Dobrushin ergodicity coefficient. The obtained results are even new in the classical and quantum settings, Comment: 29 pages

Published
2020
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8. On Certain Projections of $C^*$-Matrix Algebras

Author

Al-Rawashdeh, Ahmed

Subjects
Mathematics - Operator Algebras, 46L05, 46L80
Abstract

H. Dye defined the projections $P_{i,j}(a)$ of a $C^*$-matrix algebra by {eqnarray*} P_{i,j}(a) &=& (1+aa^*)^{-1}\otimes E_{i,i} + (1+aa^*)^{-1}a \otimes E_{i,j} + a^*(1+aa^*)^{-1} \otimes E_{j,i} + a^*(1+aa^*)^{-1}a\otimes E_{j,j}, {eqnarray*} and he used it to show that in the case of factors not of type $I_{2n}$, the unitary group determines the algebraic type of that factor. We study these projections and we show that in $\mathbb{M}_2(\mathbb{C})$, the set of such projections includes all the projections. For infinite $C^*$-algebra $A$, having a system of matrix units, including the Cuntz algebra $\mathcal{O}_n$, we have $A\simeq \mathbb{M}_n(A)$. M. Leen proved that in a simple, purely infinite $C^*$-algebra $A$, the *-symmetries generate $\mathcal{U}_0(A)$. We revise and modify Leen's proof to show that part of such *-isometry factors are of the form $1-2P_{i,j}(\omega),\ \omega \in \mathcal{U}(A)$. In simple, unital purely infinite $C^*$-algebras having trivial $K_1$-group, we prove that all $P_{i,j}(\omega)$ have trivial $K_0$-class. In particular, if $u\in \mathcal{U}(\mathcal{O}_n)$, then $u$ can be factorized as a product of *-symmetries, where eight of them are of the form $1-2P_{i,j}(\omega)$, Comment: 16 pages, no figures

Published
2011

9. C*-ALGEBRA-VALUED SPACES AND THE IMPACT OF MULTI-VALUED FIXED POINT THEOREMS ON HYPERBOLIC TYPE FRACTIONAL DIFFERENTIAL INCLUSIONS.

Author

RASHID, MALIHA, AL RAWASHDEH, AHMED, and MEHMOOD, NAYYAR

Subjects
*SET-valued maps, *METRIC spaces, *CONCEPT mapping, *RESEARCH personnel, *DIFFERENTIAL inclusions
Abstract

The pursuit of understanding fixed points and their applications has been significantly enhanced through the exploration of multi-valued mappings. This article introduces the concept of multi-valued mappings within C*-algebra-valued metric spaces. By utilizing the lower bound property, this study extends the Banach, Kannan, and Chatterjea theorems for multi-valued mappings in such spaces (for example see [14]). Moreover, the application aspect is enriched through the provision of an existence result for AB-Caputo partial hyperbolic type fractional differential inclusions. This result enhances the applicability of such inclusions, bridging the gap between theory and application. The paper concludes by offering few open problems that set the stage for future researchers in this field. The results presented here not only generalize numerous findings in the existing literature but also offer new insights into this area of research. [ABSTRACT FROM AUTHOR]

Published
2024
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12. New Fixed Point Theorems for θ−ω−Contraction on λ,μ-Generalized Metric Spaces.

Author

Kari, Abdelkarim and Al-Rawashdeh, Ahmed

Subjects
*METRIC spaces, *CONTRACTIONS (Topology), *INTEGRAL equations, *LINEAR equations
Abstract

In this paper, we consider a new extension of the Banach contraction principle, which is called the θ − ω − contraction inspired by the concept of θ − contraction in λ , μ -generalized metric spaces and to study the existence and uniqueness of fixed point for the mappings in metric space. Moreover, we discuss some illustrative examples to highlight the improvements that were made, and we also give an iterated application of linear integral equations. [ABSTRACT FROM AUTHOR]

Published
2023
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13. C*-algebra-valued measure of non-compactness with applications.

Author

Shaheen, Fouzia, Mehmood, Nayyar, and Al Rawashdeh, Ahmed

Subjects
MEASUREMENT, ALGEBRA
Abstract

In this article a novel concept of C*-algebra-valued measure of non-compactness is defined. Using this concept, the well known fixed point theorems of Darbo, Sadovskii and Krasnoslskii are generalized. We present non-trivial examples and applications to validate the real utilization of our results. [ABSTRACT FROM AUTHOR]

Published
2023
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17. Fixed Point Results for α,⊥F-Contractions in Orthogonal F-Metric Spaces with Applications

Author

Ahmad, Jamshaid, Al-Rawashdeh, Ahmed Saleh, and Al-Mazrooei, Abdullah Eqal

Subjects
Article Subject
Abstract

The main objective of this article is to introduce the notion of α,⊥F-contraction in the setting of orthogonal F-metric space and present some new fixed point results in such newly introduced space. We also furnish an example to manifest the originality of the obtained results. As application of our foremost result, we look into the solution of a nonlinear fractional differential equation.

Published
2022
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19. Common fixed point results in F-metric spaces with application to nonlinear neutral differential equation.

Author

Zahed, Hanadi, Al-Rawashdeh, Ahmed, and Ahmad, Jamshaid

Subjects
FIXED point theory, METRIC spaces, NONLINEAR differential equations, CONTRACTIONS (Topology), DIRECTED graphs
Abstract

The aim of this article is to obtain common fixed point results for generalized contractions involving control functions of two variables in the context of F-metric spaces. We also furnish an example to show the originality of our main result. Some results in the context of F-metric space equipped with a directed graph G are also established. As an application, we discuss the existence of solution to nonlinear neutral differential equation. [ABSTRACT FROM AUTHOR]

Published
2023
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33. Non-isomorphic $C^{*}$-algebras with isomorphic unitary groups

Author

Al-Rawashdeh, Ahmed

Subjects
$C^{*}$-algebra, isomorphism, 46L05, unitary group, 46L35
Abstract

H. Dye proved that the discrete unitary group in a factor determines the algebraic type of the factor. Afterwards, for a large class of simple unital $C^{*}$-algebras, Al-Rawashdeh, Booth and Giordano proved that the algebras are $*$-isomorphic if and only if their unitary groups are isomomorphic as abstract groups. In this paper, we give a counter example in the non-simple case. Indeed, we give two $C^{*}$-algebras with isomorphic unitary groups but the algebras themselves are not $*$-isomorphic.

Published
2016

34. Induced Mappings on Boolean Algebras of Clopen Sets and on Projections of the C*-Algebra C(X)

Author

AL-RAWASHDEH, Ahmed S., Al-Rawashdeh, Ahmed, and Shatanawi, Wasfi

Subjects
Unitary,Projections,Almost Isomorphisms,Boolean Algebra,Clopen Subset
Abstract

For a compact space X, any group automorphism j of C(X,S1) induces a mapping Q on the Boolean algebra of the clopen subsets of X. We prove that the disjointness of Q equivalent to qj is an orthoisomorphism on the sets of projections of the C*-algebra C(X), when j(-1)=-1. Indeed, Q is a Boolean isomorphism iff qj preserves the product of projections. If X is equipped with a probability measure m, on a certain s-algebra of X, we show (under some condition) that Q preserves the disjoint of clopen subsets, up to sets of measure zero, or equivalently, the mapping qj is m-orthoisomorphism on the projections of the C*-algebra C(X).

Published
2014

35. DQF - CONTRACTION AND RELATED FIXED POINT RESULTS IN DQM SPACES WITH APPLICATIONS.

Author

SHOAIB, ABDULLAH, RASHAM, TAHAIR, and AL-RAWASHDEH, AHMED

Subjects
SET-valued maps, FIXED point theory, CONTRACTIONS (Topology), INTEGRAL equations, SEQUENCE spaces, MATHEMATICAL mappings, SPACE
Abstract

In this article, we establish fixed point results for a pair of multivalued mappings satisfying generalized DQF-contraction on a sequence in DQM space. An example and an application to the solution of system of integral equations have been given. Our theorems improve/extend the results of Rasham et al. (J. Fixed Point Theory Appl., 20: Article 45, 2018). [ABSTRACT FROM AUTHOR]

Published
2019

36. Order-isomorphism and a projection's diagram of C(X)

Author

AL-RAWASHDEH, Ahmed S.

Subjects
Commutative C*-algebras, projections order-isomorphism, infinite projections, clopen subsets
Abstract

A mapping between projections of C*-algebras preserving the orthogonality, is called an orthoisomorphism. We define the order-isomorphism mapping on C*-algebras, and using Dye's result, we prove in the case of commutative unital C*-algebras that the concepts; order-isomorphism and the orthoisomorphism coincide. Also, we define the equipotence relation on the projections of C(X); indeed, new concepts of finiteness are introduced. The classes of projections are represented by constructing a special diagram, we study the relation between the diagram and the topological space X. We prove that an order-isomorphism, which preserves the equipotence of projections, induces a diagram-isomorphism; also if two diagrams are isomorphic, then the C*-algebras are isomorphic.

Published
2014

38. The unitary group as an invariant of a simple unital C*-algebra

Author

Al-Rawashdeh, Ahmed

Subjects
Mathematics::Operator Algebras, Mathematics
Abstract

In 1954, H. Dye proved that the unitary groups of von Neumann factors not of type I2n determine the algebraic type of factors. Using Dye's result, M. Broise showed that any isomorphism between the unitary groups of two von Neumann factors not of type In is implemented by a linear or a conjugate linear *-isomorphism between the factors. Using Dye's approach, A. Booth proved that two simple unital AF-algebras are isomorphic if and only if their unitary groups are (algebraically) isomorphic. In the first part of this thesis, we extend Booth's result to a larger class of amenable unital C*-algebras. If ϕ is an isomorphism between the unitary groups of two unital C*-algebras, it induces a bijective map &thgr;ϕ between the sets of projections of the algebras. For some UHF-algebras, we construct an automorphism ϕ of their unitary group, such that &thgr;ϕ does not preserve the orthogonality of projections. For a large class of unital C*-algebras, we show that &thgr;ϕ is always an orthoisomorphism. This class includes in particular the Cuntz algebras On , 2 ≤ n ≤ infinity, and the simple unital AF-algebras having 2-divisible K0-group. If ϕ is a continuous automorphism of the unitary group of a UHF-algebra A, we show that ϕ is implemented by a linear or a conjugate linear *-automorphism of A.

Published
2013
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41. Existence of fixed points for γ-FG-contractive condition via cyclic (α, β)-admissible mappings in b-metric spaces.

Author

Padhan, Saroj Kumar, Jagannadha Rao, G. V. V., Al-Rawashdeh, Ahmed, Nashine, Hemant Kumar, and Agarwal, Ravi P.

Subjects
METRIC spaces, MATHEMATICAL mappings, FIXED point theory
Abstract

In this paper, we introduce a new concept of cyclic (α, β)-type γ-FG-contractive mapping and we prove some fixed point theorems for such mappings in complete b-metric spaces. Suitable examples are introduced to verify the main results. As an application, we obtain sufficient conditions for the existence of solutions for nonlinear integral equation which are illustrated by an example. [ABSTRACT FROM AUTHOR]

Published
2017
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44. COMMON FIXED POINT THEOREMS FOR JS- CONTRACTIONS.

Author

AL-RAWASHDEH, AHMED and AHMAD, JAMSHAID

Subjects
*FIXED point theory, *CONTRACTIONS (Topology), *METRIC spaces, *BANACH spaces, *NONLINEAR analysis
Abstract

The aim of this article is to study JS-contractions and to establish some new common fixed point theorems for these contractions in the setup of complete metric spaces. Presented theorems are generalizations of recent fixed point theorems due to Hussain et al. [Fixed Point Theory and Applications (2015) 2015:185]. An example is also given to support our generalized result. [ABSTRACT FROM AUTHOR]

Published
2016

45. On common fixed points for α - F-contractions and applications.

Author

Al-Rawashdeh, Ahmed, Aydi, Hassen, Felhi, Abdelbasset, Sahmim, Slah, and Shatanawi, Wasfi

Subjects
METRIC spaces, DYNAMIC programming, INTEGRAL equations
Abstract

In this paper, we introduce the concept of modified F-contractions via α-admissible pair of mappings. We also provide several common fixed point results in the setting of metric spaces. Moreover, we present some illustrated examples and we give two applications on a dynamic programming and an integral equation. [ABSTRACT FROM AUTHOR]

Published
2016
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50. THE (p, q)-ABSOLUTELY SUMMING OPERATORS ON THE KÖTHE BOCHNER FUNCTION SPACES.

Author

KHANDAQJI, MONA and AL-RAWASHDEH, AHMED

Subjects
*ABSOLUTELY summing operators, *BOCHNER'S theorem, *FUNCTION spaces, *BANACH lattices, *MATHEMATICAL inequalities
Abstract

This paper is devoted to study some properties of the class of positive (p, q)-absolutely summing operators from a Banach lattice into a Banach space. We shall obtain a new characterization of such operators and generalize some inequalities on the Köthe Bochner function spaces. [ABSTRACT FROM AUTHOR]

Published
2015

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