STRONG CONVERGENCE THEOREMS FOR A FINITE FAMILY OF ASYMPTOTICALLY QUASI-NONEXPANSIVE-TYPE NONSELF-MAPPINGS IN BANACH SPACES

Abstract

In this paper, we introduce and study a new type of multistep iterative sequence with errors for a finite family of asymptotically quasi-nonexpansive-type nonself-mappings in Banach spaces. The strong convergence of a multistep iterative scheme with errors to a common fixed point of a finite family of asymptotically quasi-nonexpansive-type nonself-mappings on a nonempty closed convex subset of a real Banach space is proved. Furthermore, a sufficient condition for convergence of the iteration process to a common fixed point of mappings under our setting is also established in a real uniformly convex Banach space. The results obtained in this paper extend and improve the several recent results in this area.