Convergence Analysis of Quasi-Variational Inclusion and Fixed Point Problems of Finite Family of Certain Nonlinear Mappings in Hilbert Spaces

Abstract

The purpose of this paper is to present a modified Halpern iterative algorithm for finding a common solution of quasi-variational inclusion problem and fixed point problem of a finite family of demimetric mappings and quasi-nonexpansive mapping in the framework of real Hilbert spaces. Using our iterative algorithm, we state and prove a strong convergence theorem for approximating the solution of the aforementioned problems. We give some consequences of our main result, present an application to variational inequality problem and dispaly numerical example to show the behaviour of our result. Our result complements and extends some related results in literature.