Mutually Nearest Points for Two Sets in Metric Spaces

Porosity of mutually nearest and mutually furthest points in Banach spaces

Let X be a real strictly convex and Kadec Banach space and G a nonempty closed relatively boundedly weakly compact subset of X : Let BðX Þ (resp. KðXÞ) be the family of nonempty bounded closed (resp. compact) subsets of X endowed with the Hausdorff distance and let BGðXÞ denote the closure of the set fAABðX Þ : A-G 1⁄4 |g and KGðX Þ 1⁄4 BGðX Þ-KðXÞ: We introduce the admissible family A of BðX Þ...

Testing Properties of Sets of Points in Metric Spaces

Given query access to a set of points in a metric space, we wish to quickly check if it has a specific property. More precisely, we wish to distinguish sets of points that have the property from those that need to have at least an ε fraction of points modified to achieve it. We show one-sided error testers that immediately follow from known characterizations of metric spaces. Among other things...

Coincidence Points and Common Fixed Points for Expansive Type Mappings in $b$-Metric Spaces

The main purpose of this paper is to obtain sufficient conditions for existence of points of coincidence and common fixed points for a pair of self mappings satisfying some expansive type conditions in $b$-metric spaces. Finally, we investigate that the equivalence of one of these results in the context of cone $b$-metric spaces cannot be obtained by the techniques using scalarization function....

Common Fixed Points of Two Commuting Mappings in Complete Metric Spaces

Stationary Points for Set-valued Mappings on Two Metric Spaces

We give stationary point theorems of set-valued mappings in complete and compact metric spaces. The results in this note generalize a few results due to Fisher. 2000 Mathematics Subject Classification. 54H25.