Generalized Mixed Equilibria, Variational Inclusions, and Fixed Point Problems

Abstract

We propose two iterative algorithms for finding a common element of the set of solutions of finite generalized mixed equilibrium problems, the set of solutions of finite variational inclusions for maximal monotone and inverse strong monotone mappings, and the set of common fixed points of infinite nonexpansive mappings and an asymptotically κ-strict pseudocontractive mapping in the intermediate sense in a real Hilbert space. We prove some strong and weak convergence theorems for the proposed iterative algorithms under suitable conditions.