Weak convergence theorems for nonexpansive mappings in Banach spaces
Reads0
Chats0
TLDR
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.About:
This article is published in Journal of Mathematical Analysis and Applications.The article was published on 1979-02-01 and is currently open access. It has received 746 citations till now. The article focuses on the topics: Weak convergence & Unconditional convergence.read more
Citations
More filters
Journal ArticleDOI
Iterative Algorithms for Nonlinear Operators
TL;DR: In this paper, a modification of Rockafellar's proximal point algorithm is obtained and proved to be always strongly convergent, and the ideas of these algorithms are applied to solve a quadratic minimization problem.
Journal ArticleDOI
Strong convergence theorems for resolvents of accretive operators in Banach spaces
Journal ArticleDOI
Strong convergence of Krasnoselskii and Mann's type sequences for one-parameter nonexpansive semigroups without Bochner integrals
TL;DR: In this article, Krasnoselskii and Mann's type convergence theorems for nonexpansive semigroups without using Bochner integral and without assuming the strict convexity of Banach spaces were proved.
Book ChapterDOI
The Hybrid Steepest Descent Method for the Variational Inequality Problem over the Intersection of Fixed Point Sets of Nonexpansive Mappings
TL;DR: The hybrid steepest descent (HST) method as mentioned in this paper is a simple algorithmic solution to the variational inequality problem defined over the nonempty intersection of multiple fixed point sets of nonexpansive mappings in a real Hilbert space.
Journal ArticleDOI
Weak and strong convergence theorems for strict pseudo-contractions in hilbert spaces
Giuseppe Marino,Hong-Kun Xu +1 more
TL;DR: Nakajo and Takahashi as mentioned in this paper showed that strong convergence for nonexpansive mappings to strict pseudo-contractions can be obtained by modifying Mann's algorithm by applying projections onto suitably constructed closed convex sets to get an algorithm which generates a strong convergent sequence.
References
More filters
Journal ArticleDOI
Semicontractive and semiaccretive nonlinear mappings in Banach spaces
TL;DR: In this article, the authors present an existence theory for solutions of nonlinear functional equations in uniformly convex Banach spaces X involving nonexpansive and accretive mappings.
Journal ArticleDOI
A simple proof of the mean ergodic theorem for nonlinear contractions in Banach spaces
TL;DR: 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.
Journal ArticleDOI
A Note on Segmenting Mann Iterates
TL;DR: In this article, the authors introduced the following general iterative procedure: Suppose A = (a& is an infinite, lower triangular, regular row-stochastic matrix) and T is a continuous mapping of E into itself and xi E E, then M(x,, A, T) is the process defined by Mann.
Journal ArticleDOI
Almost convergence and nonlinear ergodic theorems
TL;DR: The first ergodic theorems for nonlinear nonexpansive mappings and semigroups in Hilbert space were established by Baillon and BrCzis as discussed by the authors.