Parallel Hybrid Algorithm for Solving Pseudomonotone Equilibrium and Split Common Fixed Point Problems

Abstract

Using the concept of Bregman W-mapping, we propose a parallel hybrid extragradient algorithm for approximating a common element of the set of solutions of pseudomonotone equilibrium problems and split common fixed point problems of Bregman weak relatively nonexpansive mappings. With the algorithm, we state and prove a strong convergence result for finding a common solution of finite family of equilibrium problem and split common fixed point problem in a real Banach space. The stepsize for the split common fixed point problem is chosen in such a way that the algorithm does not require a prior estimation of the operator norm. Finally, we present an application of our results to variational inequality problems. Our result improves and extends some existing results in the literature in these directions.