The Experts below are selected from a list of 20064 Experts worldwide ranked by ideXlab platform
C E Chidume - One of the best experts on this subject based on the ideXlab platform.
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Convergence theorems of subgradient extragradient algorithm for solving variational inequalities and a Convex feasibility problem
SpringerOpen, 2018Co-Authors: C E Chidume, M. O. NnakweAbstract:Abstract Let C be a nonempty closed and Convex Subset of a uniformly smooth and 2-uniformly Convex real Banach space E with dual space E∗ $E^{*}$. In this paper, a Krasnoselskii-type subgradient extragradient iterative algorithm is constructed and used to approximate a common element of solutions of variational inequality problems and fixed points of a countable family of relatively nonexpansive maps. The theorems proved are improvement of the results of Censor et al. (J. Optim. Theory Appl. 148:318–335, 2011)
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strong and convergence theorems for common fixed points of a finite family of multivalued demicontractive mappings in cat spaces
Abstract and Applied Analysis, 2014Co-Authors: C E Chidume, A U Bello, P NdambomveAbstract:Let K be a nonempty closed and Convex Subset of a complete CAT(0) space. Let , be a family of multivalued demicontractive mappings such that . A Krasnoselskii-type iterative sequence is shown to -converge to a common fixed point of the family . Strong convergence theorems are also proved under some additional conditions. Our theorems complement and extend several recent important results on approximation of fixed points of certain nonlinear mappings in CAT spaces. Furthermore, our method of the proof is of special interest.
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convergence theorems for a common fixed point of a finite family of nonself nonexpansive mappings
Fixed Point Theory and Applications, 2005Co-Authors: C E Chidume, Habtu Zegeye, Naseer ShahzadAbstract:Let be a nonempty closed Convex Subset of a reflexive real Banach space which has a uniformly Gâteaux differentiable norm. Assume that is a sunny nonexpansive retract of with as the sunny nonexpansive retraction. Let , , be a family of nonexpansive mappings which are weakly inward. Assume that every nonempty closed bounded Convex Subset of has the fixed point property for nonexpansive mappings. A strong convergence theorem is proved for a common fixed point of a family of nonexpansive mappings provided that , , satisfy some mild conditions.
Mohamed A Khamsi - One of the best experts on this subject based on the ideXlab platform.
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browder and gohde fixed point theorem for monotone nonexpansive mappings
Fixed Point Theory and Applications, 2016Co-Authors: Buthinah Bin A Dehaish, Mohamed A KhamsiAbstract:Let X be a Banach space or a complete hyperbolic metric space. Let C be a nonempty, bounded, closed, and Convex Subset of X and $T: C \rightarrow C$ be a monotone nonexpansive mapping. In this paper, we show that if X is a Banach space which is uniformly Convex in every direction or a uniformly Convex hyperbolic metric space, then T has a fixed point. This is the analog to Browder and Gohde’s fixed point theorem for monotone nonexpansive mappings.
Barbara Dembin - One of the best experts on this subject based on the ideXlab platform.
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the maximal flow from a compact Convex Subset to infinity in first passage percolation on mathbb z d
Annals of Probability, 2020Co-Authors: Barbara DembinAbstract:We consider the standard first passage percolation model on $\mathbb{Z}^{d}$ with a distribution $G$ on $\mathbb{R}^{+}$ that admits an exponential moment. We study the maximal flow between a compact Convex Subset $A$ of $\mathbb{R}^{d}$ and infinity. The study of maximal flow is associated with the study of sets of edges of minimal capacity that cut $A$ from infinity. We prove that the rescaled maximal flow between $nA$ and infinity $\phi (nA)/n^{d-1}$ almost surely converges toward a deterministic constant depending on $A$. This constant corresponds to the capacity of the boundary $\partial A$ of $A$ and is the integral of a deterministic function over $\partial A$. This result was shown in dimension $2$ and conjectured for higher dimensions by Garet in (Annals of Applied Probability19 (2009) 641–660).
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The maximal flow from a compact Convex Subset to infinity in first passage percolation on Z^d
2018Co-Authors: Barbara DembinAbstract:We consider the standard first passage percolation model on Z^d with a distribution G on R+ that admits an exponential moment. We study the maximal flow between a compact Convex Subset A of R^d and infinity. The study of maximal flow is associated with the study of sets of edges of minimal capacity that cut A from infinity. We prove that the rescaled maximal flow between nA and infinity φ(nA)/n^ (d−1) almost surely converges towards a deterministic constant depending on A. This constant corresponds to the capacity of the boundary ∂A of A and is the integral of a deterministic function over ∂A. This result was shown in dimension 2 and conjectured for higher dimensions by Garet in [6].
Ngaiching Wong - One of the best experts on this subject based on the ideXlab platform.
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approximating fixed points of α nonexpansive mappings in uniformly Convex banach spaces and cat 0 spaces
Fixed Point Theory and Applications, 2013Co-Authors: Eskandar Naraghirad, Ngaiching WongAbstract:An existence theorem for a fixed point of an α-nonexpansive mapping of a nonempty bounded, closed and Convex Subset of a uniformly Convex Banach space has been recently established by Aoyama and Kohsaka with a non-constructive argument. In this paper, we show that appropriate Ishikawa iterate algorithms ensure weak and strong convergence to a fixed point of such a mapping. Our theorems are also extended to CAT(0) spaces. AMS Subject Classification: 54E40; 54H25; 47H10; 37C25
Buthinah Bin A Dehaish - One of the best experts on this subject based on the ideXlab platform.
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browder and gohde fixed point theorem for monotone nonexpansive mappings
Fixed Point Theory and Applications, 2016Co-Authors: Buthinah Bin A Dehaish, Mohamed A KhamsiAbstract:Let X be a Banach space or a complete hyperbolic metric space. Let C be a nonempty, bounded, closed, and Convex Subset of X and $T: C \rightarrow C$ be a monotone nonexpansive mapping. In this paper, we show that if X is a Banach space which is uniformly Convex in every direction or a uniformly Convex hyperbolic metric space, then T has a fixed point. This is the analog to Browder and Gohde’s fixed point theorem for monotone nonexpansive mappings.
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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, Wojciech 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