Convergence of modified S-iteration process for two asymptotically quasi-nonexpansive type mappings in CAT(0) spaces

Abstract

The purpose of this paper is to study convergence of a newly defined modified S-iteration process to a common fixed point of two asymptotically quasi-nonexpansive type mappings in the setting of CAT(0) space. We give a suffcient condition for convergence to a common fixed point and establish some strong convergence theorems for the said iteration process and mappings under suitable conditions. Our results extend and improve many known results from the existing literature.

Keywords

• asymptotically quasi-nonexpansive type mapping
• strong convergence
• modified S-iteration process
• common fixed point
• CAT(0) space
• 54H25
• 54E40