On relatively contractive relations in pairs of generalized uniform spaces

• Autores: Víctor Manuel Onieva Aleixandre , J. Ruiz Fernández de Pinedo
• Localización: Revista matemática hispanoamericana, ISSN 0373-0999, Vol. 42, Nº. 4-6, 1982, págs. 194-200
• Idioma: inglés
• Títulos paralelos:
  • Sobre relaciones relativamente contractivas en pares de espacios uniformes generalizados
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• Resumen

  • 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].