Approximating Common Fixed Point of Three $C$-$\alpha$ Nonexpansive Mappings

Year 2023, Volume: 11 Issue: 2, 184 - 194, 31.10.2023

Seyit Temir , Zeynep Bayram

Abstract

In this paper, we consider a new class of nonlinear mappings presented in \cite{Shukla} that generalizes two well-known classes of nonexpansive type mappings and extends some other classes of mappings. We introduce approximating common fixed point of three C-$\alpha$ nonexpansive mappings through weak and strong convergence of an iterative sequence in a uniformly convex Banach space. We also numerically illustrate the common fixed point approximations of the presented iteration for the three $C$-$\alpha$ nonexpansive mappings.

Keywords

Suzuki’s generalized nonexpansive mappings, α−nonexpansive mappings, Opial property, uniformly convex Banach space, common fixed point, convergence theorems.

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