Modified inertial algorithm for solving mixed equilibrium problems in Hadamard spaces

Abstract

The main purpose of this paper is to introduce the concept of modified inertial algorithm in Hadamard spaces. We emphasize that, as far as we know, this is the first time that this concept is being considered in this setting. Under some weak assumptions, we prove that the modified inertial algorithm converges strongly to a common solution of a finite family of mixed equilibrium problems and fixed point problem of a nonexpansive mapping. We also give a primary numerical illustration in the framework of Hadamard spaces, to show the efficiency of the modified inertial term in our proposed algorithm.