On Some Generalization of Multivalued Nonexpansive Mappings

Abstract

In this article, we introduce the concepts of multivalued (DL)-type and multivalued α-nonexpansive mappings in the Banach spaces. We show that these two classes of mappings properly contain some important classes of nonlinear mappings. Moreover, we compare the relationship between such classes of mappings and obtain some fixed point results. In addition, we give partial answer to the open question posed by Reich in 1983, about the relationship between fixed point property of multivalued and single-valued nonexpansive mappings. This contribution generalizes and improves some recent results in this context. © 2019, Iranian Mathematical Society.