Iterative Procedures For Finite Family Of Total Asymptotically Nonexpansive Mappings

Abstract

It is our aim in this paper to introduce an explicit iterative scheme for a finite family of total asymptotically nonexpansive mappings and prove its strong convergence to a common fixed point of these mappings in smooth reflexive real Banach spaces which admits weakly sequentially continuous duality mappings. In addition, we proved path existence theorem for finite family of asymptotically nonexpansive mappings; and further showed that the convergence of the path guarantees that the set of common fixed points of finite family of asymptotically nonexpansive mappings is a sunny nonexpansive retract. Our theorems improve, generalize and unify several recently announced results in the literature.