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W. M. Kozlowski - One of the best experts on this subject based on the ideXlab platform.
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fixed point theory in Modular Function spaces
2015Co-Authors: Mohamed A Khamsi, W. M. Kozlowski, Simeon ReichAbstract:Introduction.- Fixed Point Theory in Metric Spaces: An Introduction.- Modular Function Spaces.- Geometry of Modular Function Spaces.- Fixed Point Existence Theorems in Modular Function Spaces.- Fixed Point Construction Processes.- Semigroups of Nonlinear Mappings in Modular Function Spaces.- Modular Metric Spaces.
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on the convergence of iteration processes for semigroups of nonlinear mappings in Modular Function spaces
Fixed Point Theory and Applications, 2015Co-Authors: Buthinah Bin A Dehaish, Mohamed A Khamsi, W. M. KozlowskiAbstract:Let C be a ρ-bounded, ρ-closed, convexsubset of a Modular Function space . We investigate the problem of constructingcommon fixed points for asymptotic pointwise nonexpansive semigroups of mappings , i.e. a family such that , , and , where , for every . MSC: 47H09, 46B20, 47H10, 47E10.
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fixed point iteration processes for asymptotic pointwise nonexpansive mapping in Modular Function spaces
Fixed Point Theory and Applications, 2012Co-Authors: Buthinah Bin A Dehaish, W. M. KozlowskiAbstract:Let Lρ be a uniformly convex Modular Function space with a strong Opial property. Let T : C → C be an asymptotic pointwise nonexpansive mapping, where C is a ρ-a.e. compact convex subset of Lρ. In this paper, we prove that the generalized Mann and Ishikawa processes converge almost everywhere to a fixed point of T. In addition, we prove that if C is compact in the strong sense, then both processes converge strongly to a fixed point. MSC: Primary 47H09; Secondary 47H10
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fixed point iteration processes for asymptotic pointwise nonexpansive mapping in Modular Function spaces
Fixed Point Theory and Applications, 2012Co-Authors: Buthinah Bin A Dehaish, W. M. KozlowskiAbstract:Let L ρ Open image in new window be a uniformly convex Modular Function space with a strong Opial property. Let T : C → C Open image in new window be an asymptotic pointwise nonexpansive mapping, where C is a ρ-a.e. compact convex subset of L ρ Open image in new window. In this paper, we prove that the generalized Mann and Ishikawa processes converge almost everywhere to a fixed point of T. In addition, we prove that if C is compact in the strong sense, then both processes converge strongly to a fixed point.
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on asymptotic pointwise nonexpansive mappings in Modular Function spaces
Journal of Mathematical Analysis and Applications, 2011Co-Authors: Mohamed A Khamsi, W. M. KozlowskiAbstract:We prove the existence of fixed points of asymptotic pointwise nonexpansive mappings in Modular Function spaces.
Safeer Hussain Khan - One of the best experts on this subject based on the ideXlab platform.
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approximation of fixed point of multivalued ρ quasi contractive mappings in Modular Function spaces
Arab Journal of Mathematical Sciences, 2019Co-Authors: Godwin Amechi Okeke, Safeer Hussain KhanAbstract:Abstract The purpose of this paper is to extend the recent results of Okeke et al. (2018) to the class of multivalued ρ -quasi-contractive mappings in Modular Function spaces. We approximate fixed points of this class of nonlinear multivalued mappings in Modular Function spaces. Moreover, we extend the concepts of T -stability, almost T -stability and summably almost T -stability to Modular Function spaces and give some results.
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approximating fixed points of left lambda rho right λ ρ firmly nonexpansive mappings in Modular Function spaces
Arabian Journal of Mathematics, 2018Co-Authors: Safeer Hussain KhanAbstract:In this paper, we first introduce an iterative process in Modular Function spaces and then extend the idea of a $$\lambda $$ -firmly nonexpansive mapping from Banach spaces to Modular Function spaces. We call such mappings as $$ \left( \lambda ,\rho \right) $$ -firmly nonexpansive mappings. We incorporate the two ideas to approximate fixed points of $$\left( \lambda ,\rho \right) $$ -firmly nonexpansive mappings using the above-mentioned iterative process in Modular Function spaces.
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iterative approximation of fixed point of multivalued quasi nonexpansive mappings in Modular Function spaces with applications
Journal of Function Spaces and Applications, 2018Co-Authors: Godwin Amechi Okeke, S A Bishop, Safeer Hussain KhanAbstract:Recently, Khan and Abbas initiated the study of approximating fixed points of multivalued nonlinear mappings in Modular Function spaces. It is our purpose in this study to continue this recent trend in the study of fixed point theory of multivalued nonlinear mappings in Modular Function spaces. We prove some interesting theorems for -quasi-nonexpansive mappings using the Picard-Krasnoselskii hybrid iterative process. We apply our results to solving certain initial value problem.
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Iterative Approximation of Fixed Point of Multivalued ρ-Quasi-Nonexpansive Mappings in Modular Function Spaces with Applications
Hindawi Limited, 2018Co-Authors: Godwin Amechi Okeke, S A Bishop, Safeer Hussain KhanAbstract:Recently, Khan and Abbas initiated the study of approximating fixed points of multivalued nonlinear mappings in Modular Function spaces. It is our purpose in this study to continue this recent trend in the study of fixed point theory of multivalued nonlinear mappings in Modular Function spaces. We prove some interesting theorems for ρ-quasi-nonexpansive mappings using the Picard-Krasnoselskii hybrid iterative process. We apply our results to solving certain initial value problem
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approximating fixed points of multivalued ρ nonexpansive mappings in Modular Function spaces
Fixed Point Theory and Applications, 2014Co-Authors: Safeer Hussain Khan, Mujahid AbbasAbstract:The existence of fixed points of single-valued mappings in Modular Function spaces has been studied by many authors. The approximation of fixed points in such spaces via convergence of an iterative process for single-valued mappings has also been attempted very recently by Dehaish and Kozlowski (Fixed Point Theory Appl. 2012:118, 2012). In this paper, we initiate the study of approximating fixed points by the convergence of a Mann iterative process applied on multivalued ρ-nonexpansive mappings in Modular Function spaces. Our results also generalize the corresponding results of (Dehaish and Kozlowski in Fixed Point Theory Appl. 2012:118, 2012) to the case of multivalued mappings. MSC: 47H09; 47H10; 54C60
Buthinah Bin A Dehaish - One of the best experts on this subject based on the ideXlab platform.
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On Monotone Asymptotic Pointwise Nonexpansive Mappings in Modular Function Spaces
Hindawi Limited, 2019Co-Authors: Buthinah Bin A DehaishAbstract:In this work, we investigate the existence of the fixed points of a monotone asymptotic pointwise nonexpansive mapping defined in a Modular Function space. Our result extends the fixed point result of Khamsi and Kozlowski
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on the convergence of iteration processes for semigroups of nonlinear mappings in Modular Function spaces
Fixed Point Theory and Applications, 2015Co-Authors: Buthinah Bin A Dehaish, Mohamed A Khamsi, W. M. KozlowskiAbstract:Let C be a ρ-bounded, ρ-closed, convexsubset of a Modular Function space . We investigate the problem of constructingcommon fixed points for asymptotic pointwise nonexpansive semigroups of mappings , i.e. a family such that , , and , where , for every . MSC: 47H09, 46B20, 47H10, 47E10.
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fixed point iteration processes for asymptotic pointwise nonexpansive mapping in Modular Function spaces
Fixed Point Theory and Applications, 2012Co-Authors: Buthinah Bin A Dehaish, W. M. KozlowskiAbstract:Let Lρ be a uniformly convex Modular Function space with a strong Opial property. Let T : C → C be an asymptotic pointwise nonexpansive mapping, where C is a ρ-a.e. compact convex subset of Lρ. In this paper, we prove that the generalized Mann and Ishikawa processes converge almost everywhere to a fixed point of T. In addition, we prove that if C is compact in the strong sense, then both processes converge strongly to a fixed point. MSC: Primary 47H09; Secondary 47H10
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fixed point iteration processes for asymptotic pointwise nonexpansive mapping in Modular Function spaces
Fixed Point Theory and Applications, 2012Co-Authors: Buthinah Bin A Dehaish, W. M. KozlowskiAbstract:Let L ρ Open image in new window be a uniformly convex Modular Function space with a strong Opial property. Let T : C → C Open image in new window be an asymptotic pointwise nonexpansive mapping, where C is a ρ-a.e. compact convex subset of L ρ Open image in new window. In this paper, we prove that the generalized Mann and Ishikawa processes converge almost everywhere to a fixed point of T. In addition, we prove that if C is compact in the strong sense, then both processes converge strongly to a fixed point.
Mohamed A Khamsi - One of the best experts on this subject based on the ideXlab platform.
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fixed point theory in Modular Function spaces
2015Co-Authors: Mohamed A Khamsi, W. M. Kozlowski, Simeon ReichAbstract:Introduction.- Fixed Point Theory in Metric Spaces: An Introduction.- Modular Function Spaces.- Geometry of Modular Function Spaces.- Fixed Point Existence Theorems in Modular Function Spaces.- Fixed Point Construction Processes.- Semigroups of Nonlinear Mappings in Modular Function Spaces.- Modular Metric Spaces.
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on the convergence of iteration processes for semigroups of nonlinear mappings in Modular Function spaces
Fixed Point Theory and Applications, 2015Co-Authors: Buthinah Bin A Dehaish, Mohamed A Khamsi, W. M. KozlowskiAbstract:Let C be a ρ-bounded, ρ-closed, convexsubset of a Modular Function space . We investigate the problem of constructingcommon fixed points for asymptotic pointwise nonexpansive semigroups of mappings , i.e. a family such that , , and , where , for every . MSC: 47H09, 46B20, 47H10, 47E10.
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topics in fixed point theory
2014Co-Authors: Saleh A Almezel, Qamrul Hasan Ansari, Mohamed A KhamsiAbstract:1 Introduction to Metric Fixed Point Theory. M.A. Khamsi.- 2 Banach Contraction Principle and its Generalizations. Abdul Latif.- 3 Ekeland's Variational Principle and Its Extensions with Applications. Qamrul Hasan Ansari.- 4 Fixed Point Theory in Hyperconvex Metric Spaces. Rafael Espinola and Aurora Fernandez-Leon.- 5 An Introduction to Fixed Point Theory in Modular Function Spaces. W. M. Kozlowski.- 6 Fixed Point Theory in Ordered Sets from the Metric Point of View. M. Z. Abu-Sbeih and M. A. Khamsi.- 7 Some Fundamental Topological Fixed Point Theorems for Set-Valued Maps. Hichem Ben-El-Mechaiekh.- 8 Some Iterative Methods for Fixed Point Problems. Q. H. Ansari and D. R. Sahu.- Index.
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on asymptotic pointwise nonexpansive mappings in Modular Function spaces
Journal of Mathematical Analysis and Applications, 2011Co-Authors: Mohamed A Khamsi, W. M. KozlowskiAbstract:We prove the existence of fixed points of asymptotic pointwise nonexpansive mappings in Modular Function spaces.
Mujahid Abbas - One of the best experts on this subject based on the ideXlab platform.
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approximating fixed points of multivalued ρ nonexpansive mappings in Modular Function spaces
Fixed Point Theory and Applications, 2014Co-Authors: Safeer Hussain Khan, Mujahid AbbasAbstract:The existence of fixed points of single-valued mappings in Modular Function spaces has been studied by many authors. The approximation of fixed points in such spaces via convergence of an iterative process for single-valued mappings has also been attempted very recently by Dehaish and Kozlowski (Fixed Point Theory Appl. 2012:118, 2012). In this paper, we initiate the study of approximating fixed points by the convergence of a Mann iterative process applied on multivalued ρ-nonexpansive mappings in Modular Function spaces. Our results also generalize the corresponding results of (Dehaish and Kozlowski in Fixed Point Theory Appl. 2012:118, 2012) to the case of multivalued mappings. MSC: 47H09; 47H10; 54C60