A Note on Homotopic Invariance for Endpoints of Multi-Valued Contractive Mappings

Bancha Panyanak

Abstract

In this paper, we prove the homotopic invariance for endpoints of multi-valued contractive mappings in Banach spaces. We also give an example to illustrate the main result. At the same time, a question raised in [B. Panyanak, The demiclosed principle for multi-valued nonexpansive mappings in Banach spaces, J. Nonlinear Convex Anal. 17 (2016) 2063--2070] is answered in the negative.