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 commonfixed point of a family of generalized nonexpansive mappings and then prove astrong convergence theorem for a family of generalized nonexpansive mappings inBanach spaces. Using this theorem, we obtain some new results for a generalizednonexpansive mapping and two generalized nonexpansive mappings in Banachspaces. Moreover, we apply our main result to obtain a strong convergence theoremfor a family of nonexpansive mappings in a Hilbert space.