A fixed point theorem in generalized metric spaces

• Autorzy: Kikina L. , Kikina K.
• Języki publikacji: EN

Abstrakty

EN

A generalized metric space has been defined by Branciari as a metric space in which the triangle inequality is replaced by a more general inequality. Subsequently, some classical metric fixed point theorems have been transferred to such a space. In this paper, we continue in this direction and prove a version of Fisher’s fixed point theorem in generalized metric spaces.

Słowa kluczowe

EN

Cauchy sequence; generalized metric spaces; fixed point; implicit relation

PL

ciąg Cauchy'ego; przestrzeń metryczna; punkt stały; relacja ukryta

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2013
• Tom: Vol. 46, nr 1
• Strony: 181--190
• Opis fizyczny: Bibliogr. 10 poz.

Twórcy

autor

Kikina L.

• Department of Mathematics and Computer Science, Faculty of Natural Sciences, University of Gjirokastra, Albania

autor

Kikina K.

• Department of Mathematics and Computer Science, Faculty of Natural Sciences, University of Gjirokastra, Albania

Bibliografia

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• [3] A. Branciari, A fixed point theorem of Banach-Caccippoli type on a class of generalized metric spaces, Publ. Math. Debrecen 57 (2000), 31–37.
• [4] P. Das, A fixed point theorem on a class of generalized metric spaces, Korean J. Math. Sciences 1 (2002), 29–33.
• [5] P. Das, L. K. Dey, A fixed point theorem in a generalized metric space, Soochow J. Math. 33 (2007), 33–39.
• [6] B. Fisher, Related fixed point on two metric spaces, Math. Sem. Notes, Kobe Univ. 10 (1982), 17–26.
• [7] R. Kannan, Some results on fixed points II, Amer. Math. Monthly 76 (1969), 405–408.
• [8] B. E. Rhoades, A comparison of various definitions of contractive mappings, Trans. Amer. Math. Soc. 226 (1977), 256–290.
• [9] S. Reich, Some remarks concerning contraction mappings, Canad. Math. Bull. 14 (1971), 121–124.
• [10] I. R. Sarma, J. M. Rao, S. S. Rao, Contractions over generalized metric spaces, J. Nonlinear Sci. Appl. 2 (2009), 108–182.