Fixed Point Theorems for Some Generalized Multi-Valued Nonexpansive Mappings in Hadamard Spaces

Chayanit Klangpraphan, Bancha Panyanak

Abstract

We show that a condition on mappings introduced by Bunlue andSuantai is weaker than the notion of nonexpansive mappings and stronger than the notion of quasi-nonexpansive mappings. We also obtain the demiclosed principleas well as a fixed point theorem for the class of mappings satisfying this condition. A convergence theorem of the Ishikawa iteration for discontinuous quasi-nonexpansive mappings is also given.