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A fixed point theorem for nonexpansive compact self-mapping

T. D. Narang (2014)

Annales UMCS, Mathematica

A mapping T from a topological space X to a topological space Y is said to be compact if T(X) is contained in a compact subset of Y . The aim of this paper is to prove the existence of fixed points of a nonexpansive compact self-mapping defined on a closed subset having a contractive jointly continuous family when the underlying space is a metric space. The proved result generalizes and extends several known results on the subject

A fixed point theorem for non-self multi-maps in metric spaces

Bapurao Chandra Dhage (1999)

Commentationes Mathematicae Universitatis Carolinae

A fixed point theorem is proved for non-self multi-valued mappings in a metrically convex complete metric space satisfying a slightly stronger contraction condition than in Rhoades [3] and under a weaker boundary condition than in Itoh [2] and Rhoades [3].

A fixed-point anomaly in the plane

Charles L. Hagopian, Janusz R. Prajs (2005)

Fundamenta Mathematicae

We define an unusual continuum M with the fixed-point property in the plane ℝ². There is a disk D in ℝ² such that M ∩ D is an arc and M ∪ D does not have the fixed-point property. This example answers a question of R. H. Bing. The continuum M is a countable union of arcs.

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