On relatively contractive relations in pairs of generalized uniform spaces

J.C. Mathews and D.W. Curtis have introduced some structures which generalize structures of uniform types to the product of two sets, and they obtain a generalized version of Banach's contraction mapping theorem. In this note we prove that these structures are obtained from the usual analogues by means of a particular bijection; hence we do not have a meaningful generalization. For example, this bijection provides, from a result by A. S. Davies, an analogue of Banach's well-known contraction mapping theorem which trivially implies the main result of [4].

El Instituto "Jorge Juan" de Matemáticas del CSIC se integraría posteriormente en el Instituto de Matemáticas y Física Fundamental (IMAFF).

Peer reviewed

Country

Spain

Related Organizations

Spanish National Research Council
Spain

Keywords

Conectores, Fixed-point and coincidence theorems (topological aspects), Uniform structures and generalizations, F-estructura, Filtros, Espacios cuasiuniformes, uniform structures, Espacio uniforme generalizado, Multifunción

Impact byBIP!

	selected citations These citations are derived from selected sources. This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).	0
	popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.	Average
	influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).	Average
	impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.	Average