Strong Convergence of the Shrinking Projection Method for the Split Equilibrium Problem and an Infinite Family of Relatively Nonexpansive Mappings in Banach spaces

Nutchari Niyamosot, Warunun Inthakon

Abstract

In this paper, we use the shrinking projection method to prove a strong convergence theorem for finding a common solution of the split equilibrium problem and fixed point problem of a relatively quasi−nonexpansive mapping. Consequently, our main theorem can apply to find a common solution of the split equilibrium problem and common fixed point problem for an infinite family of relatively nonexpansive mappings in Banach spaces.