A novel framework for solving pseudomonotone equilibrium and fixed point problems using bregman techniques

The application of a Bregman subgradient extragradient algorithm to pseudomonotone equilibrium and fixed points problems associated with quasi-Bregman nonexpansive mappings is considered. We incorporate a Bregman distance framework and an inertial extrapolation technique to approximate a common solution to both the equilibrium problem and the fixed points of quasi-Bregman nonexpansive mappings within a reflexive Banach space. In addition, we introduce a regulating parameter, denoted by $$\eta $$ , to regulate and enhance the step size of the algorithm such that the cost operator does not rely on the Lipschitz constant. We verify the accuracy and effectiveness of our approach with two numerical examples. We note that the incorporation of our parameter $$\eta $$ improves the convergence rate compared to other algorithms. Also, we observed that the smaller the value of $$\eta $$ , the faster the convergence. These results demonstrate the effectiveness of our algorithm and provide contributions that advance existing knowledge in this research domain.