Extragradient Algorithm for Solving Pseudomonotone Equilibrium Problem with Bregman Distance in Reflexive Banach Spaces

Using the Bregman distance technique, we study the approximation of solution of pseudomonotone equilibrium problem using modified extragradient method in a real reflexive Banach space. Our proposed method involves a non-increasing self-adaptive stepsize rule and prove a weak convergence result without any prior estimate of the Lipschitz-like constants of the equilibrium bifunction under some appropriate conditions in a real reflexive Banach space. Some application to generalized Nash equilibrium problem in differential games is given. Finally, we give numerical examples to compare the performance of our method with other related methods in the literature and illustrate our method using various types of Bregman distance functions.