An Iterative Method for Approximating the Common Solutions of Nonexpansive Semigroups, a System of Variational Inequalities, Variational Inequalities and Equilibrium Problems
Meng Wen *
Department of Mathematics, Hubei Normal University, Huangshi, 435002, P.R.China
Changsong Hu
Department of Mathematics, Hubei Normal University, Huangshi, 435002, P.R.China
*Author to whom correspondence should be addressed.
Abstract
In this work, we consider an general iterative method for finding a common element of the set of common fixed points of a one-parameter nonexpansive semigroup problem, a system of variational inequality problems, a variational inequality problem and the set of solutions of a suitable equilibrium problem in a real Hilbert space. Further we establish a strong convergence theorem based on this method. Our results improve and extend corresponding ones announced by many others.
Keywords: Nonexpansive semigroup, Equilibrium problem, Variational inequality problem, System of variational inequality problems, Projection