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Mann Iteration of Weak Convergence Theorems in
Liang-gen Hu,Jin-ping Wang +1 more
- 01 Jan 2009
2
TL;DR: In this paper, the authors used Mann's iteration process to establish weak convergence theorems for approximating a fixed point of kstrictly pseudocontractive mappings with respect to p in puniformly convex Banach spaces.
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Abstract: In this paper, by using Mann's iteration process we will establish several weak convergence theorems for approximating a fixed point of kstrictly pseudocontractive mappings with respect to p in puniformly convex Banach spaces. Our results answer partially the open question proposed by Marino and Xu, and extend Reich's theorem from nonexpansive mappings to kstrict pseudocontractive mappings.
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Citations
Strong convergence of iterative algorithms with variable coefficients for generalized equilibrium problems, variational inequality problems and fixed point problems
Ci-Shui Ge,Neng-Fu Yu,Lin Zhao +2 more
TL;DR: In this article, the authors proposed some new iterative algorithms with variable coefficients for finding a common element of the set of solutions of a generalized equilibrium problem, set of solution of the variational inequality problem for a monotone, Lipschitz-continuous mapping and set of common fixed points of a finite family of asymptotically κ-strict pseudocontractive mappings.
Iterative process for a strictly pseudo-contractive mapping in uniformly convex Banach spaces
Yu Zhou,Haiyun Zhou,Peiyuan Wang +2 more
TL;DR: In this article, the weak convergence of strictly pseudo-contractive mapping in a p-uniformly convex Banach space with more relaxed restrictions on the parameters is studied.
References
Iterative construction of fixed points of asymptotically nonexpansive mappings
TL;DR: In this paper, a completely continuous and asymptotically nonexpansive self-mapping of a nonempty closed bounded and convex subset of a Hilbert space is studied, where the sequence defined by xn + 1:= αnTn(xn) + (1 − αn) x n converges strongly to some fixed point of T under certain conditions.
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.