A BREGMAN HYBRID EXTRAGRADIENT METHOD FOR SOLVING PSEUDOMONOTONE EQUILIBRIUM AND FIXED POINT PROBLEMS

In this paper, using the concept of the Bregman distance, we propose a Bregman extragradient method for finding a common solution of a finite family of pseudomonotone equilibrium problems and the common fixed point problem of a finite family of Bregman relatively nonexpansive mappings. We introduce a generalized step size such that the algorithm does not require a prior knowledge of the operator norm. A strong convergence theorem was proved in the setting of reflexive Banach spaces and applied to variational inequality problems. Furthermore, we present some numerical examples to illustrate the consistency and accuracy of our algorithm and also to compare with the results in the literature.