Fixed point theorems for some generalized multi-valued nonexpansive mappings in Hadamard spaces

Abstract

© 2019 by the Mathematical Association of Thailand. All rights reserved. We show that a condition on mappings introduced by Bunlue and Suantai is weaker than the notion of nonexpansive mappings and stronger than the notion of quasi-nonexpansive mappings. We also obtain the demiclosed principle as 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.