Document Type : Original Article

Authors

• Junaid Ahmad ¹
• Kifayat Ullah ²
• Muhammad Safi Ullah Khan ²
• Naseer Muhammad ²

¹ Department of Mathematics, Uuniversity of Science and Technology,Bannu 28100, Khyber Pakhtunkhwa, Pakistan

² Department of Mathematics, University of Science and Technology, Bannu 28100, Khyber Pakhtunkhwa, Pakistan

Abstract

In this paper, we study endpoints of multi-valued generalized $\alpha$-nonexpansive mappings in Banach spaces. Under some appropriate assumptions, we prove that the sequence of modified Agarwal-O'Rega-Sahu iterative process defined by Abdeljawad et al. (2020) converges strongly to an endpoint of a multi-valued generalized $\alpha$-nonexpansive mappings. We also give an illustrate example. Our results are new and extend the corresponding results of the current literature.

Keywords

• Endpoint
• S iteration
• generalized $alpha$-nonexpansive mapping
• condition $(J)$
• Banach space