Strong convergence algorithm for the split problem of variational inclusions, split generalized equilibrium problem and fixed point problem

Abstract

The purpose of this paper is to recommend an iterative scheme to approximate a common element of the solution sets of the split problem of variational inclusions, split generalized equilibrium problem and fixed point problem for non-expansive mappings. We prove that the sequences generated by the recommended iterative scheme strongly converge to a common element of solution sets of stated split problems. In the end, we provide a numerical example to support and justify our main result. The result studied in this paper generalizes and extends some widely recognized results in this direction.

Algorithms for Approximating Solutions of Split Variational Inclusion and Fixed-Point Problems

“…There are various ways to solve the split problems, see [2][3][4][5][6][7][8][9][10][11][12][13]. To solve (3), a remarkable channel brought up by Censor and Segal [14] is of the manner:…”