An algorithm for finding a common solution for a system of mixed equilibrium problem, quasi-variational inclusion problem and fixed point problem of nonexpansive semigroup

Abstract

In this paper, we introduce a hybrid iterative scheme for finding a common element of the set of solutions for a system of mixed equilibrium problems, the set of common fixed points for a nonexpansive semigroup and the set of solutions of the quasi-variational inclusion problem with multi-valued maximal monotone mappings and inverse-strongly monotone mappings in a Hilbert space. Under suitable conditions, some strong convergence theorems are proved. Our results extend some recent results in the literature.

Keywords

• nonexpansive semigroup
• mixed equilibrium problem
• viscosity approximation method
• quasi-variational inclusion problem
• multi-valued maximal monotone mappings
• \(\alpha\)-inverse-strongly monotone mapping