Strong convergence theorems by monotone hybrid method for a family of generalized nonexpansive mappings in Banach spaces

Abstract

In this paper, we study monotone hybrid method for finding a common fixed point of a family of generalized nonexpansive mappings and then prove a strong convergence theorem for a family of generalized nonexpansive mappings in Banach spaces. Using this theorem, we obtain some new results for a generalized nonexpansive mapping and two generalized nonexpansive mappings in Banach spaces. Moreover, we apply our main result to obtain a strong convergence theorem for a family of nonexpansive mappings in a Hilbert space.