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

Abstract

<abstract><p>This paper reports a modified F-iterative process for finding the fixed points of three generalized $ \alpha $-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 $ \alpha $-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 $ \alpha $-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 $ \alpha $-nonexpansive mappings. The main finding of the paper is new and extends many known results of the literature.</p></abstract>