On relatively contractive relations in pairs of generalized uniform spaces.

Onieva Aleixandre, Víctor M., and Ruiz Fernández de Pinedo, Javier. "On relatively contractive relations in pairs of generalized uniform spaces. ." Revista Matemática Hispanoamericana 42.4-5-6 (1982): 194-200. <http://eudml.org/doc/39820>.

@article{OnievaAleixandre1982,
abstract = {J. C. Mathews and D. W. Curtis, [4], 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, [1], an analogue of Banach's well-known contraction mapping theorem which trivially implies the main result of [4].},
author = {Onieva Aleixandre, Víctor M., Ruiz Fernández de Pinedo, Javier},
journal = {Revista Matemática Hispanoamericana},
keywords = {Espacio uniforme generalizado; Conectores; Filtros; Espacios cuasiuniformes; Multifunción; F-estructura; uniform structures},
language = {eng},
number = {4-5-6},
pages = {194-200},
title = {On relatively contractive relations in pairs of generalized uniform spaces. },
url = {http://eudml.org/doc/39820},
volume = {42},
year = {1982},
}

TY - JOUR
AU - Onieva Aleixandre, Víctor M.
AU - Ruiz Fernández de Pinedo, Javier
TI - On relatively contractive relations in pairs of generalized uniform spaces.
JO - Revista Matemática Hispanoamericana
PY - 1982
VL - 42
IS - 4-5-6
SP - 194
EP - 200
AB - J. C. Mathews and D. W. Curtis, [4], 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, [1], an analogue of Banach's well-known contraction mapping theorem which trivially implies the main result of [4].
LA - eng
KW - Espacio uniforme generalizado; Conectores; Filtros; Espacios cuasiuniformes; Multifunción; F-estructura; uniform structures
UR - http://eudml.org/doc/39820
ER -