Strong convergence theorems for a common point of solution of variational inequality, solutions of equilibrium and fixed point problems

Abstract

We introduce an iterative process which converges strongly to a common point of solution of variational inequality problem for continuous monotone mapping, solution of equilibrium problem and a common fixed point of finite family of asymptotically regular uniformly continuous relatively asymptotically nonexpansive mappings in Banach spaces. Our scheme does not involve computation of C n+1 from C n for each n ≥ 1. Our theorems improve and unify most of the results that have been proved for this important class of nonlinear operators. Mathematics Subject Classification (2000): 47H05, 47H09, 47H10, 47J05, 47J25

Iterative methods for a fixed point of hemicontractive-type mapping and a solution of a variational inequality problem

“…Variational inequality theory, which was first introduced by Stampacchia [13] in 1964, emerged as an interesting and fascinating branch of applicable mathematics with a wide range of applications in economics, industry, network analysis, optimizations, pure and applied sciences etc. In recent years, much attention has been given to developing efficient iterative methods for treating solution problems of variational inequalities [3,21,25] and the references therein. The classical variational inequality is equivalent to a fixed point problem.…”

Strong Convergence Theorems for Quasi-Bregman Nonexpansive Mappings in Reflexive Banach Spaces

“…The set of solutions of (47) is denoted by EP( ). Equilibrium problem is a unified model of several problems, namely, variational inequality problem, complementary problem, saddle point problem, optimization problem, fixed point problem, and so forth; see [20,30,[38][39][40][41][42][43].…”

Strong convergence theorems for solutions of fixed point and variational inequality problems

“…All authors read and approved the final manuscript. 1 School of Mathematics and Physics, North China Electric Power University, Baoding, 071003, China.…”