scholarly journals Strong Convergence of a Hybrid Iteration Scheme for Equilibrium Problems, Variational Inequality Problems and Common Fixed Point Problems, of Quasi-ϕ-Asymptotically Nonexpansive Mappings in Banach Spaces

2012 ◽  
Vol 2012 ◽  
pp. 1-19 ◽  
Author(s):  
Jing Zhao
Keyword(s):  
Variational Inequality ◽  
Strong Convergence ◽  
Banach Spaces ◽  
Nonexpansive Mappings ◽  
Monotone Mapping ◽  
Common Fixed Points ◽  
Iteration Scheme ◽  
Common Element ◽  
Asymptotically Nonexpansive Mappings ◽  
Asymptotically Nonexpansive

We introduce an iterative algorithm for finding a common element of the set of common fixed points of a finite family of closed quasi-ϕ-asymptotically nonexpansive mappings, the set of solutions of an equilibrium problem, and the set of solutions of the variational inequality problem for aγ-inverse strongly monotone mapping in Banach spaces. Then we study the strong convergence of the algorithm. Our results improve and extend the corresponding results announced by many others.

scholarly journals Convergence of two-step iterative scheme with errors for two asymptotically nonexpansive mappings

2004 ◽  
Vol 2004 (37) ◽  
pp. 1965-1971 ◽  
Author(s):  
Hafiz Fukhar-ud-din ◽  
Safeer Hussain Khan
Keyword(s):  
Strong Convergence ◽  
Fixed Points ◽  
Banach Spaces ◽  
Iterative Scheme ◽  
Nonexpansive Mappings ◽  
Common Fixed Points ◽  
Weak And Strong Convergence ◽  
Asymptotically Nonexpansive Mappings ◽  
Asymptotically Nonexpansive ◽  
The Common

A two-step iterative scheme with errors has been studied to approximate the common fixed points of two asymptotically nonexpansive mappings through weak and strong convergence in Banach spaces.

scholarly journals On Unification of the Strong Convergence Theorems for a Finite Family of Total Asymptotically Nonexpansive Mappings in Banach Spaces

2012 ◽  
Vol 2012 ◽  
pp. 1-21 ◽  
Author(s):  
Farrukh Mukhamedov ◽  
Mansoor Saburov
Keyword(s):  
Strong Convergence ◽  
Banach Spaces ◽  
Nonexpansive Mappings ◽  
Common Fixed Points ◽  
Nonempty Closed Convex Subset ◽  
Finite Family ◽  
Convergence Theorems ◽  
Asymptotically Nonexpansive Mappings ◽  
Asymptotically Nonexpansive ◽  
Total Asymptotically Nonexpansive Mappings

We unify all known iterative methods by introducing a new explicit iterative scheme for approximation of common fixed points of finite families of total asymptoticallyI-nonexpansive mappings. Note that such a scheme contains a particular case of the method introduced by (C. E. Chidume and E. U. Ofoedu, 2009). We construct examples of total asymptotically nonexpansive mappings which are not asymptotically nonexpansive. Note that no such kind of examples were known in the literature. We prove the strong convergence theorems for such iterative process to a common fixed point of the finite family of total asymptoticallyI-nonexpansive and total asymptotically nonexpansive mappings, defined on a nonempty closed-convex subset of uniformly convex Banach spaces. Moreover, our results extend and unify all known results.

scholarly journals A New Hybrid Algorithm for a Pair of Quasi--Asymptotically Nonexpansive Mappings and Generalized Mixed Equilibrium Problems in Banach Spaces

2011 ◽  
Vol 2011 ◽  
pp. 1-22
Author(s):  
Jinhua Zhu ◽  
Shih-Sen Chang
Keyword(s):  
Strong Convergence ◽  
Nonexpansive Mappings ◽  
Convex Banach Space ◽  
Generalized Mixed Equilibrium Problem ◽  
Common Element ◽  
Strong Convergence Theorem ◽  
Asymptotically Nonexpansive Mappings ◽  
Asymptotically Nonexpansive ◽  
Generalized Mixed Equilibrium ◽  
Mixed Equilibrium

The purpose of this paper is, by using a new hybrid method, to prove a strong convergence theorem for finding a common element of the set of solutions for a generalized mixed equilibrium problem, the set of solutions for a variational inequality problem, and the set of common fixed points for a pair of quasi--asymptotically nonexpansive mappings. Under suitable conditions some strong convergence theorems are established in a uniformly smooth and strictly convex Banach space with Kadec-Klee property. The results presented in the paper improve and extend some recent results.

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