FIXED POINT THEOREMS FOR NONEXPANSIVE MAPPINGS WITH APPLICATIONS TO GENERALIZED EQUILIBRIUM AND SYSTEM OF NONLINEAR VARIATIONAL INEQUALITIES PROBLEMS

Yeol Je  Cho; Narin Petrot; Suthep  Suantai

FIXED POINT THEOREMS FOR NONEXPANSIVE MAPPINGS WITH APPLICATIONS TO GENERALIZED EQUILIBRIUM AND SYSTEM OF NONLINEAR VARIATIONAL INEQUALITIES PROBLEMS

Authors

Yeol Je Cho DEPARTMENT OFMATHEMATICSEDUCATION AND THERINS, GYEONGSANGNATIONALUNIVERSITY, CHINJU660-701, KOREA
Narin Petrot DEPARTMENT OFMATHEMATICS, FACULTY OFSCIENCE, NARESUANUNIVERSITY, PHITSANULOK, 65000,THAILAND
Suthep Suantai DEPARTMENT OFMATHEMATICS, FACULTY OFSCIENCE, CHIANGMAIUNIVERSITY, CHIANGMAI, 50200,THAILAND

Keywords:

Generalized equilibrium problem, system of nonlinear variational inequalities, nonexpansive mapping, strict pseudo-contraction mappings

Abstract

In this paper, a method for finding the common element of two nonexpansive mappings are provided. Consequently, we provide some results for the fixed points of an infinite family of nonexpansive mappings and of an infinite family of strict pseudo-contraction mappings. Furthermore, we apply our main result to the problems of finding the solution of generalized equilibrium and system of nonlinear variational inequalities problems. Some interesting remarks will be also pointed out and discussed.