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.
Cite this paper as:
R. Precup, Le théorème des contractions dans des espaces syntopogènes, Anal. Numér. Théor. Approx., 9 (1980) no. 1, pp. 113-123 (in French).
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Academia Republicii S.R.
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MR: 82i:54008.
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References
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[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.