In this paper, we introduce a linesearch algorithm for solving fixed points of Bregman quasi asymptotically nonexpansive multivalued mappings and pseudomonotone equilibrium problem in reflexive Banach space. Using the linesearch method, we prove a strong convergence of the iterative scheme to a common point in the set of solutions of some equilibrium problem and common fixed point of the finite family of Bregman quasi asymptotically nonexpansive multivalued mappings with out imposing Bregman Lipschitz condition on the bifunction $g$ as used by many authors in the extragradient method. Our results improve and generalize many recent results in the literature. پرونده مقاله

In this paper, we introduce a new hybrid extragradient-type algorithm for approximating an element in the set of common solutions of equilibrium problems and common fixed points of family of Bregman demigeneralized mappings which is also a common zero of the sum of maximal monotone and Bregman inverse strongly monotone operators in the setting of reflexie Banach space. Strong convergence of the proposed algorithm to a solutions of the said problems is established which improves and generalizes many recently announced results in the literature. پرونده مقاله