A new modified iterative scheme for finding common fixed points in Banach spaces: application in variational inequality problems

Abstract

This paper reports a modified F-iterative process for finding the fixed points of three generalized α-nonexpansive mappings. We assume certain assumptions to establish the weak and strong convergence of the scheme in the context of a Banach space. We suggest a numerical example of generalized α-nonexpansive mappings which exceeds, properly, the category of functions furnished with a condition (C). After that, we show that our modified F-iterative scheme of this example converges to a common fixed point of three generalized α-nonexpansive mappings. As an application of our main findings, we suggest a new projection-type iterative scheme to solve variational inequality problems in the setting of generalized α-nonexpansive mappings. The main finding of the paper is new and extends many known results of the literature.

Keywords

• f-iteration
• common fixed point
• generalized α-nonexpansive mapping
• convergence
• condition (ⅰ)