Nonexpansive mappings defined on unbounded domains

Nonexpansive Mappings Defined on Unbounded Domains

In the study of nonexpansive mappings and fixed point theory the domain of the mapping is usually assumed to be bounded or, as in certain approximation results (see, e.g., [20]), fixed points are assumed to exist. However in [21] Penot used uniform asymptotic concepts which he had earlier introduced in [22] to extend the Browder-Göhde-Kirk theorem to unbounded sets. The term “asymptotic” is use...

Metric fixed point theory for nonexpansive mappings defined on unbounded sets

*Correspondence: [email protected] 3Department of Mathematics, King Abdulaziz University, P.O. Box 80203, Jeddah, 21589, Saudi Arabia Full list of author information is available at the end of the article Abstract It is standard practice in metric fixed point theory to reduce fixed point questions for mappings defined on unbounded sets to the bounded case. Many of these results are couched in...

Generic convergence of infinite products of nonexpansive mappings with unbounded domains

Citation: Reich S and Zaslavski AJ (2015) Generic convergence of infinite products of nonexpansive mappings with unbounded domains. We study the generic convergence of infinite products of nonexpansive mappings with unbounded domains in hyperbolic metric spaces.

On Firmly Nonexpansive Mappings

It is shown that any A-firmly, 0 < A < 1 , nonexpansive mapping T: C —> C has a fixed point in C whenever C is a finite union of nonempty, bounded, closed convex subsets of a uniformly convex Banach space. Let C be a nonempty subset of a Banach space X, and let X £ (0, 1). Then a mapping T: C —> X is said to be X-firmly nonexpansive if (1) \\Tx Ty\\ < ||(1 X)(x y)+X(Tx Ty)\\ for all x, y £ C. I...

On Multivalued Nonexpansive Mappings in ℝ-Trees