Journal ArticleDOI
A simple proof of the mean ergodic theorem for nonlinear contractions in Banach spaces
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In this article, it was shown that if E is a uniformly rotund Banach space with a Frechet differentiable norm, and C is a bounded nonempty closed convex subset of E, and T: C→C is a contraction, then the iterates {Tnx} are weakly almost-convergent to a fixed-point of T.Abstract:
The following theorem is proven:if E is a uniformly rotund Banach space with a Frechet differentiable norm, C is a bounded nonempty closed convex subset of E, and T: C→C is a contraction, then the iterates {Tnx} are weakly almost-convergent to a fixed-point of T.read more
Citations
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Weak convergence theorems for nonexpansive mappings in Banach spaces
TL;DR: In this paper, it was shown that a closed convex subset of a Banach space is weakly almost convergent if (~~~~ xick)/n y uniformly in k, and an operator A C E x E is said to be m-accretive if R(.Z + -4) = E and /.x-x~] <~~~-~~+v(y,-y~)~ for ally,EAZx,, i=l,2, andr>O.
Journal ArticleDOI
A concept of convergence in geodesic spaces
William A. Kirk,Bancha Panyanak +1 more
TL;DR: The notion of weak convergence in CAT(0) spaces was introduced by Lim and Kuczumow as discussed by the authors, where each geodesic triangle is at least as thin as its comparison triangle in the Euclidean plane.
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A variable Krasnosel'skii?Mann algorithm and the multiple-set split feasibility problem
TL;DR: In this paper, a variable Krasnosel'skii?Mann algorithm was used to solve the multiple-set split feasibility problem in infinite-dimensional Hilbert spaces.
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Fixed point iteration processes for asymptotically nonexpansive mappings
Kok-Keong Tan,Hong-Kun Xu +1 more
TL;DR: In this article, the modified Mann and Ishikawa iteration processes defined by xn+, = tnTnxn+I-tn)xn and xn+ i = tNTn(snTnexn+snI-sn)xN) +(-tn) xn 7 respectively, converge weakly to a fixed point of T.
Journal ArticleDOI
Weak and strong convergence theorems for three-step iterations with errors for asymptotically nonexpansive mappings☆
TL;DR: In this article, several weak and strong convergence theorems are established for the three-step iterative schemes with errors for asymptotically nonexpansive mappings.
References
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On the almost-convergence of iterates of a nonexpansive mapping in Hilbert space and the structure of the weak ω-limit set
TL;DR: In this paper, the weak ω-limit set of iterates of a self-mapping of a closed convex subset C of a real Hilbert space is studied, and conditions under which it is invariant under T are established.