A shrinking projection extragradient algorithm for equilibrium problem and fixed point problem

Abstract

In this paper, a shrinking projection algorithm based on the extragradient iteration method for finding a common element of the set of common fixed points of a finite family of asymptotically nonexpansive mappings and a generalized nonexpansive set-valued mapping and the set of solutions of equilibrium problem for pseudomonotone and Lipschitz-type continuous bifunctions is introduced and investigated in Hilbert spaces. Moreover, the strong convergence of the sequence generated by the proposed algorithm is derived under some suitable assumptions. These results are new and develop some recent results in this field.