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 nding a common solution to a xed point problem involving a nite family of -demimetric operators and a split monotone inclusion problem with monotone and Lipschitz continuous operator in real Hilbert spaces. Motivated by the inertial technique and the Tseng method, a new and e cient 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.