Several inertial methods for solving split convex feasibilities and related problems

Abstract

In this paper, we study the problem of finding a common solution to an equilibrium and split convex feasibility problems in real Hilbert spaces. Inspired and motivated by classical as well as recent works in this field, we introduce several simple inertial self-adaptive algorithms for solving this problem. Convergence of the algorithms is given under mild and standard assumptions and a theoretical application of the problem for solving an equilibrium and proximal split convex feasibility problems is presented. Primary numerical experiments in finite and infinite dimensional spaces illustrate the performances of the proposed methods.