Le théorème des contractions dans des espaces syntopogènes

Abstract

The Banach contraction theorem for metric spaces has been generalized for local convex spaces by G. Marinescu [7] and then by I. Colojoara [6] and N. Gheorghiu [6] for uniform spaces.
In this paper we give a fixed point theorem of the same type as that of Banach, for even more general spaces: the syntopogene spaces; an extension of this theorem for the case of multivalued mappings is also given.

English title

The contraction theorem in syntopogens spaces

Authors

Keywords

syntopogene spaces.

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Cite this paper as:

R. Precup, Le théorème des contractions dans des espaces syntopogènes, Rev. Anal. Numér. Théor. Approx., 9 (1980) no. 1, pp. 113-123 (in French).

About this paper

Journal
Mathematica, Revue d’Analyse Numerique et de Theorie de l’Approximation
Publisher Name

Academia Republicii S.R.

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MR: 82i:54008.

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References

[1] Avramescu, C.  Teoreme de punct fix pentru aplicaţii multivoce contractante definite în spaţii uniforme. analele Univ. Craiova, 1, 63-67, 1970.

[2] Bărbulescu, I., On a fixed point theorem for multivalued mappings in uniform spaces. (Romanian. English summary) An. Univ. Craiova Ser. a V-a No. 2, 73-77. (1974), MR0415589.

[3] Berge, Claude, Espaces topologiques: Fonctions multivoques. (French) Collection Universitaire de Mathématiques, Vol. III Dunod, Paris 1959 xi+272 pp., MR0105663.

[4] Colojoară, Ion, Sur un théorème de point fixe dans les espaces uniformes complets. (Romanian. Russian, French summary) Com. Acad. R. P. Romîne 11 1961 281-283, MR0143192.

[5] Császár, Á., Fondaments de la topologie générale, Gauthier-Villars, Paris, 1960.

[6] Gheorghiu, N., Contraction theorem in uniform spaces. (Romanian) Stud. Cerc. Mat. 19 1967 119-122, MR0247498.

[7] Marinescu, G., Spaţii vectoriale topologice şi pseudotopologice. (Romanian) [Topological and pseudo-topological vector spaces] Biblioteca Matematică, IV Editura Academiei Republicii Populare Romîne, Bucharest 1959 217 pp., MR0107803.

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