ON FINITE FAMILY OF MONOTONE VARIATIONAL INCLUSION PROBLEMS IN REFLEXIVE BANACH SPACE

Abstract

The main purpose of this paper is to study monotone variational inclusion problems in a reflexive real Banach space. We propose a Halpern-type algorithm and prove that the sequence generated by it converges strongly to a common solution of a finite family of monotone vairiational inclusion problems in a reflexive real Banach space. We then apply our results to solve a finite family of variational inequality problems and convex feasibility problem.