An inertial parallel iterative method for solving generalized mixed equilibrium problems and common fixed point problem in reflexive Banach spaces

Abstract

By combining the shrinking projection method with the parallel splitting-up technique and the inertial term, we introduce a new inertial parallel iterative method for finding common solutions of a finite system of generalized mixed equilibrium problems and common fixed points of a finite family of Bregman totally quasi-asymptotically nonexpansive mappings. After that, we prove a strong convergence result for the proposed iteration in reflexive Banach spaces. By this theorem, we obtain some convergence results for generalized mixed equilibrium problems in reflexive Banach spaces. In addition, we give a numerical example to illustrate the proposed iterations. The obtained results are improvements and extensions to some known results in this area.