Strong and weak convergence theorems for general mixed equilibrium problems and variational inequality problems and fixed point problems in Hilbert spaces

Abstract

In this paper, we introduce two iterative algorithms for finding a common element of the set of solutions of finite general mixed equilibrium problems and the set of solutions of finite variational inequalities for inverse strongly monotone mappings and the set of common fixed points of an asymptotically k-strictly pseudocontractive mapping in the intermediate sense in a real Hilbert space. We prove some strong and weak convergence theorems by using the proposed algorithms under some suitable conditions. Our results improve and extend the corresponding results announced by many others.