Common solutions for a monotone variational inequality problem and an infinite family of inverse strongly monotone non-self operators

Abstract

In this paper, we introduce regularization methods for finding a point, being not only a solution for a monotone variational inequality problem but also a common zero for an infinite family of inverse strongly monotone non-self operators of a closed convex subset in a real Hilbert space. In these methods, only a finite number of the operators is used at each iteration step. Applications to the problem of common fixed point for an infinite family of strictly pseudo-contractive non-self operators and the split feasibility and fixed point problems are considered. As a particular case, a regularization extragradient iterative method without prior knowledge of operator norms for solving the split feasibility problem (SFP) is obtained. Numerical examples are given for illustration.