This paper is intended to introduce the standard three-step iteration algorithm to approximate endpoints of nonexpansive multi-valued mapping in the Banach spaces framework. Some weak and strong results under appropriate conditions for the iterative sequence generated by the proposed process convergence outcomes are discussed. In general, the results improve and unify some of Panyanak’s recent analysis (J. Fixed Point Theory Appl. (2018)). © 2021. NSP Natural Sciences Publishing Cor. All Rights Reserved.