S. Temir†
Abstract: In this paper, we study multi‑valued generalized α‑nonexpansive mappings in uniformly convex Banach spaces. We introduce a new multi‑valued iterative process and prove some weak and strong convergence results in uniformly convex Banach space. We also study the stability of this iteration process. Further, we provide a numerical example of the multi‑valued generalized α‑nonexpansive mapping; finally, the convergence of this iteration process to the fixed point for multi‑valued generalized α‑nonexpansive mapping is discussed on this numerical example.
MSC: 47H010; 54H25.
keywords: Generalized α‑nonexpansive mappings, multi‑valued mapping, fixed point, iteration process, uniformly convex Banach spaces.
DOI 10.56082/annalsarscimath.2023.1-2.554
†seyittemir@adiyaman.edu.tr, Adıyaman University, Department of Mathematics, Faculty of Arts and Science, Adıyaman, Turkey.
PUBLISHED in Annals Academy of Romanian Scientists Series on Mathematics and Its Application, Volume 15 no 1-2, 2023
