# On relatively contractive relations in pairs of generalized uniform spaces.

Víctor M. Onieva Aleixandre; Javier Ruiz Fernández de Pinedo

Revista Matemática Hispanoamericana (1982)

- Volume: 42, Issue: 4-5-6, page 194-200
- ISSN: 0373-0999

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topOnieva 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 -

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