The demiclosed principle for multi-valued nonexpansive mappings in Banach spaces

Abstract

© Copyright 2016. In this paper, we prove the demiclosed principle for multi-valued nonexpansive mappings in uniformly convex Banach spaces. As consequences, we obtain the homotopic invariance for fixed points of both single-valued and multivalued nonexpansive mappings. One of our main results gives an affirmative answer to a question raised by Kirk (2003).