A NEW RELAXED TSENG METHOD FOR FINDING A COMMON SOLUTION OF FIXED POINT AND SPLIT MONOTONE INCLUSION PROBLEMS

Abstract

In this paper, we study the problem of finding a common solution to a fixed pointproblem involving a finite family of ρ-demimetric operators and a split monotone inclusion problem with monotone and Lipschitz continuous operator in real Hilbert spaces. Motivatedby the inertial technique and the Tseng method, a new and efficient iterative method for solving the aforementioned problem is introduced and studied. Also, we establish a strong convergence result of the proposed method under standard and mild conditions.