Strong Convergence Theorems for Generalized Equilibrium Problems, Variational Inequality and Fixed Point Problems of Asymptotically Strict Pseudocontractive Mappings in the Intermediate Sense

Jing Zhao, Songnian He, Qiao-li Dong

Abstract

In this paper, we introduce two iterative schemes based on the extragradient method and hybrid projection method for finding a common element of the set of a generalized equilibrium problem, the set of solutions of the variational inequality problem for a γ-inverse strongly monotone mapping and the set of fixed points of an asymptotically κ-strict pseudocontractive mappings in the intermediate sense which is not necessarily Lipschitzian in a real Hilbert space. We prove that two sequences converge strongly to a common element of the above three sets under some parameters controlling conditions. Our results improve and extend the corresponding results announced by many others.