VISCOSITY EXTRAGRADIENT METHOD WITH ARMIJO LINESEARCH RULE FOR PSEUDOMONOTONE EQUILIBRIUM PROBLEM AND FIXED POINT PROBLEM IN HILBERT SPACES

Abstract

In this paper, we introduce a viscosity extragradient method with Armijo linesearch rule to find a common element of solution set of a pseudomonotone equilibrium problem and fixed point set of a nonexpansive nonself-mapping in Hilbert space. The strong convergence of the algorithm is proved. As the application, a common fixed point theorem for two nonexpansive nonself-mappings is proved. Finally, some numerical examples are given to illustrate the effectiveness of the algorithm. Our result improves the ones of others in the literature.