Types of Fixed Points of Set-Valued Contraction Mappings for Comparable Elements

Characterization of weak fixed point property for new class of set-valued nonexpansive mappings

In this paper, we introduce a new class of set-valued mappings which is called MD-type mappings. This class of mappings is a set-valued case of a class of the D-type mappings. The class of D-type mappings is a generalization of nonexpansive mappings that recently introduced by Kaewkhao and Sokhuma. The class of MD-type mappings includes upper semi-continuous Suzuki type mappings, upper semi-con...

Endpoints of multi-valued cyclic contraction mappings

Endpoint results are presented for multi-valued cyclic contraction mappings on complete metric spaces (X, d). Our results extend previous results given by Nadler (1969), Daffer-Kaneko (1995), Harandi (2010), Moradi and Kojasteh (2012) and Karapinar (2011).

Fixed Point Theorems for Set-valued Mappings

On Common Fixed Points of Weakly Commuting Mappings and Set - Valued Mappings

ABS]RACT. Our main theorem establishes the uniqueness of the common fixed point of tw set-valued mappings and of two single-valued mappings defined on a complete metric space, under a contractive condition and a weak commutativity concept. This improves a theorem of the second author. Let (X,d) be a complete metric space and let B(X) be the set of all nonempty, bounded subsets of X As in [I], l...

The Homotopic Invariance for Fixed Points of Set-valued Nonexpansive Mappings*

T h e homotopic invariance of fixed points of set-valued contractions and nonexpansive mappings is studied. As application, nonlinear alternative principles are given. A LeraySchauder alternative and an antipodal theorem for set-valued nonexpansive mappings are also included.