Dynamic processes, fixed points, endpoints, asymmetric structures, and investigations related to Caristi, Nadler, and Banach in uniform spaces. (English) Zbl 1350.54021

Włodarczyk, Kazimierz; Plebaniak, Robert

Abstr. Appl. Anal. 2015, Article ID 942814, 16 p. (2015).

This paper further extends a set of results whose ultimate ancestor is Banach’s contraction mapping theorem. The metric space is permitted to be a uniform space with symmetric structure defined by families of pseudo-metrics, and the map is permitted to be a set-valued contraction. New and very general results are obtained, and some of the resulting ‘fixed point’ and ‘endpoint’ theorems are used to study dissipative set-valued dynamical systems without lower semi-continuous entropies. Some of the results obtained are new even in the classical settings of metric spaces.

Reviewer: Thomas B. Ward (Leeds)

MSC:

54E15	Uniform structures and generalizations
37C25	Fixed points and periodic points of dynamical systems; fixed-point index theory; local dynamics
26E25	Set-valued functions

Keywords:

uniform space; symmetric structure; fixed point theorem

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