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Mathematica Slovaca

Editor-in-Chief: Pulmannová, Sylvia


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Fixed point of contractive mappings in generalized metric spaces

1Jadavpur University Kolkata

2National Institute of Technology Durgapur

© 2009 Versita Warsaw. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License. (CC BY-NC-ND 3.0)

Citation Information: Mathematica Slovaca. Volume 59, Issue 4, Pages 499–504, ISSN (Online) 1337-2211, ISSN (Print) 0139-9918, DOI: 10.2478/s12175-009-0143-2, July 2009

Publication History

Published Online:
2009-07-29

Abstract

We prove a fixed point theorem for contractive mappings of Boyd and Wong type in generalized metric spaces, a concept recently introduced in [BRANCIARI, A.: A fixed point theorem of Banach-Caccioppoli type on a class of generalized metric spaces, Publ. Math. Debrecen 57 (2000), 31–37].

MSC: Primary 54H25; 47H10

Keywords: generalized metric space; contractive mapping; fixed point

  • [1] BRANCIARI, A.: A fixed point theorem of Banach-Caccioppoli type on a class of generalized metric spaces, Publ. Math. Debrecen 57 (2000), 31–37.

  • [2] BOYD, D. W.— WONG, J. S. W.: On nonlinear contraction, Proc. Amer. Math. Soc. 20 (1969), 458–464. http://dx.doi.org/10.2307/2035677 [Crossref]

  • [3] ĆIRIĆ, LJ. B.: A generalization of Banach’s contraction principle, Proc. Amer. Math. Soc. 45 (1974), 267–273. http://dx.doi.org/10.2307/2040075 [Crossref]

  • [4] DAS, P.: A fixed point theorem on a class of generalized metric spaces, Korean J. Math. Sci. 9 (2002), 29–33.

  • [5] EDELSTEIN, M.: On fixed and periodic points under contraction mappings, J. London Math. Soc. (2) 37 (1962), 74–79. http://dx.doi.org/10.1112/jlms/s1-37.1.74 [Crossref]

  • [6] LAHIRI, B. K.— DAS, P.: Fixed point of a Ljubomir Ćirić’s quasi-contraction mapping in a generalized metric space, Publ. Math. Debrecen 61 (2002), 589–594. [Web of Science]

  • [7] RAKOTCH, E.: A note on contractive mappings, Proc. Amer. Math. Soc. 13 (1962), 459–465. http://dx.doi.org/10.2307/2034961 [Crossref]

  • [8] REICH, S.— ZASLAVSKI, A. J.: Almost all non-expansive mappings are contractive, C.R. Math. Acad. Sci. Soc. R. Can. 22 (2000), 118–124.

  • [9] REICH, S.— ZASLAVSKI, A. J.: The set of non contractive mappings is σ-porous in the space of all non-expansive mappings, C. R. Math. Acad. Sci. Paris 333 (2001), 539–544.

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