Hybrid shrinking projection extragradient-like algorithms for equilibrium and fixed point problems

Abstract

Based on the extragradient-like method combined with shrinking projection, we propose two algorithms, the first algorithm is obtained using sequential computation of extragradientlike method and the second algorithm is obtained using parallel computation of extragradient-like method, to find a common point of the set of fixed points of nonexpansive mapping and the solution set of the equilibrium problem of a bifunction given as a sum of finite number of H¨older continuous bifunctions. The convergence theorems for iterative sequences generated by the algorithms are established under widely used assumptions for the bifunction and its summands.