Existence and Approximation of Fixed Points for Set-Valued Mappings

EXISTENCE OF FIXED POINTS OF CERTAIN CLASSES OF NONLINEAR MAPPINGS

In this study, we introduce the classes of $phi$-strongly pseudocontractive mappings in the intermediate sense and generalized $Phi$-pseudocontractive mappings in the intermediate sense and prove the existence of fixed points for those maps. The results generalise the results of several authors in literature including Xiang [Chang He Xiang, Fixed point theorem for generalized $Phi$-pseudocontra...

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...

Approximation of fixed points for a continuous representation of nonexpansive mappings in Hilbert spaces

This paper introduces an implicit scheme for a   continuous representation of nonexpansive mappings on a closed convex subset of a Hilbert space with respect to a   sequence of invariant means defined on an appropriate space of bounded, continuous real valued functions of the semigroup.   The main result is to    prove the strong convergence of the proposed implicit scheme to the unique solutio...

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...