Strong convergence of the shrinking projection method for the split equilibrium problem and an infinite family of relatively nonexpansive mappings in banach spaces

Abstract

© 2020 by the Mathematical Association of Thailand. 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.