Strong convergence theorems for finite families of pseudomonotone equilibrium and fixed point problems in Banach spaces

Abstract

In this article, we introduce a new linesearch technique with Halpern iteration for finding a common solution of finite families of pseudomonotone equilibrium problems and fixed point of finite family of quasi- $$\phi $$ -nonexpansive mappings in Banach spaces. Under standard assumptions imposed on the equilibrium bifunctions and the quasi- $$\phi $$ -nonexpansive mappings, we proved that the sequence generated by our algorithm converges strongly to the unique solution of the equilibrium and fixed point problems. Numerical example is presented to illustrate the efficiency and accuracy of the proposed algorithm. Our results improve and extend many existing results in the literature in this direction.