The Modified Viscosity Iteration with m-Generalized Hybrid Mappings and (a, b)-Monotone Mappings for Equilibrium Problems

Pichada Sadeewong, Teerapol Saleewong, Poom Kumam, Yeol Je Cho

Abstract

In this paper, we show the existence of a common element of the set of solutions of an equilibrium problem, the set of fixed points of m-generalized hybrid and (a, b)-monotone mappings in Hilbert spaces by using a modified viscosity iteration. First, we prove some strong convergence theorems of our proposed algorithm to converge a common element of the set of solutions of an equilibrium problem, the sets of fixed points of m-generalized hybrid and (a, b)-monotone mappings. Finally, we give numerical examples to illustrate the our results.