Watcharaporn Cholamjiak

A Hybrid Method for a Countable Family of Multivalued Maps, Equilibrium Problems, and Variational Inequality Problems

We introduce a new monotone hybrid iterative scheme for finding a common element of the set of common fixed points of a countable family of nonexpansive multivalued maps, the set of solutions of variational inequality problem, and the set of the solutions of the equilibrium problem in a Hilbert space. Strong convergence theorems of the purposed iteration are established.

Approximation of common fixed points of two quasi-nonexpansive multi-valued maps in Banach spaces

In this paper, we introduce and study two new iterative procedures with errors for two quasi-nonexpansive multi-valued maps in Banach spaces. Strong convergence theorems of the proposed iterations to a common fixed point of two quasi-nonexpansive multi-valued maps in uniformly convex Banach spaces are established.

An implicit iteration process for solving a fixed point problem of a finite family of multi-valued mappings in Banach spaces

Abstract This work is concerned with the strong convergence of an approximating common fixed point sequence of a finite family of multi-valued mappings in a uniformly convex and smooth Banach space using an implicit iteration scheme introduced by Xu and Ori [H.K. Xu, R.G. Ori, An implicit iteration process for nonexpansive mappings, Numer. Funct. Anal. Optim. 22 (2001) 767–773].

Weak and strong convergence theorems for a finite family of generalized asymptotically quasi-nonexpansive mappings

In this paper, we introduce a new iterative scheme for finding a common fixed point of a finite family of generalized asymptotically quasi-nonexpansive mappings in a uniformly convex Banach space. We establish weak and strong convergence theorems. Our main results improve and extend the corresponding ones obtained in Schu (1991) [J. Schu, Iterative construction of fixed points of asymptotically nonexpansive mapping, J. Math. Anal. Appl. 159 (1991) 407-413] and many others.

Monotone Hybrid Projection Algorithms for an Infinitely Countable Family of Lipschitz Generalized Asymptotically Quasi-Nonexpansive Mappings

We prove a weak convergence theorem of the modified Mann iteration process for a uniformly Lipschitzian and generalized asymptotically quasi-nonexpansive mapping in a uniformly convex Banach space. We also introduce two kinds of new monotone hybrid methods and obtain strong convergence theorems for an infinitely countable family of uniformly Lipschitzian and generalized asymptotically quasi-nonexpansive mappings in a Hilbert space. The results improve and extend the corresponding ones announced by Kim and Xu (2006) and Nakajo and Takahashi (2003).

A modified S-iteration process for G-nonexpansive mappings in Banach spaces with graphs

In this work, we prove the weak and strong convergence of a sequence generated by a modified S-iteration process for finding a common fixed point of two G-nonexpansive mappings in a uniformly convex Banach space with a directed graph. We also give some numerical examples for supporting our main theorem and compare convergence rate between the studied iteration and the Ishikawa iteration.

Viscosity Approximation Methods for Nonexpansive Multi-Valued Nonself Mappings and Equilibrium Problems

Abstract In this paper, strong convergence theorems by the viscosity approximation method for nonexpansive multi-valued nonself mappings and equilibrium problems are established under some suitable conditions in a Hilbert space. The obtained results extend and improve the corresponding results existed in the literature.

A HYBRID METHOD FOR A COUNTABLE FAMILY OF LIPSCHITZ GENERALIZED ASYMPTOTICALLY QUASI-NONEXPANSIVE MAPPINGS AND AN EQUILIBRIUM PROBLEM

In this paper, we introduce a new iterative scheme for finding a common element of the fixed points set of a countable family of uni- formly Lipschitzian generalized asymptotically quasi-nonexpansive map- pings and the solutions set of equilibrium problems. Some strong con- vergence theorems of the proposed iterative scheme are established by using the concept of W-mappings of a countable family of uniformly Lip- schitzian generalized asymptotically quasi-nonexpansive mappings.