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Tytuł artykułu

Probabilistic generalized metric spaces and nonlinear contractions

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Języki publikacji
EN
Abstrakty
EN
We give a probabilistic generalization of the theory of generalized metric spaces [2]. Then, we prove a fixed point theorem for a self-mapping of a probabilistic generalized metric space, satisfying the very general nonlinear contraction condition without the assumption that the space is Hausdorff.
Wydawca
Rocznik
Strony
437--452
Opis fizyczny
Bibliogr. 26 poz.
Twórcy
autor
  • National School of Applied Sciences P.O. BOX 669 Oujda University Morocco, dr.mbarki@gmail.com
autor
  • Multidisciplinary Faculty of Taroudante Ibn Zuhr University, Agadir Hay El Mohammadi (Lastah) P. O. BOX 271, 83000 Taroudant Morocco, rchdnaciri@gmail.com
Bibliografia
  • [1] A. Azam, M. Arshad, Kannan fixed point theorem on generalized metric spaces, J. Non-linear Sci. Appl. 1 (2008), 45–48.
  • [2] A. Branciari, A fixed point theorem of Banach–Caccioppoli type on a class of generalized metric spaces, Publ. Math. Debrecen 57(1–2) (2000), 31–37.
  • [3] D. W. Boyd, J. S. W. Wong, On nonlinear contractions, Proc. Amer. Math. Soc. 20 (1969), 458–464.
  • [4] P. Das, A fixed point theorem in a generalized metric space, Soochow J. Math. 33(1) (2007), 33–39.
  • [5] M. Elamrani, A. Mbarki, B. Mehdaoui, Nonlinear contarctions and semigroups in general complete probabilistic metric spaces, Panamer. Math. J. 11(4) (2001), 79–87.
  • [6] M. Frèchet, Sur quelques points du calcul fonctionnel, Rend. Circ. Mat. Palermo 22 (1906), 1–74.
  • [7] V. Gregori, A. Sapena, On fixed-point theorems in fuzzy metric spaces, Fuzzy Sets and Systems 125 (2002), 245–252.
  • [8] O. Hadzić, A fixed point theorem in Menger spaces, Publ. Inst. Math. (Beograd) 20 (1979), 107–112.
  • [9] O. Hadzić, Fixed point theorems for multivalued mappings in probabilistic metric spaces, Fuzzy Sets and Systems 88 (1997), 219–226.
  • [10] F. Hausdorff, Grudzüge der Mengenlehre, Leizig: Veit und Comp., 1914.
  • [11] J. R. Jachymski, Equivalence of some contractivity properties over metrical structures, Proc. Amer. Math. Soc. 125(8) (1997), 2327–2335.
  • [12] O. Kramosil, J. Michalek, Fuzzy metric and statistical metric spaces, Kybernetika 11 (1975), 326–334.
  • [13] L. Kikina, K. Kikina, Fixed points on two generalized metric spaces, Int. J. Math. Anal. 5(29–32) (2011), 1459–1467.
  • [14] A. Mbarki, A. Benbrik, A. Ouahab, W. Ahid, T. Ismail, Comments on "Fixed Point Theorems for φ-Contraction in Probabilistic Metric Space", Int. J. Math. Anal. 7(13) (2013), 625–635.
  • [15] K. Menger, Untersuchungen über allgemeine Metrik, Math. Ann. 100(1) (1928), 75–163.
  • [16] K. Menger, Kurventheorie, Leipzig: Teubner (Reprinted by Chelsea Publ. Co., Bronx. NY., 1932).
  • [17] K. Menger, Statistical metrics, Proc. Natl. Acad. Sci. 28 (1942), 535–537.
  • [18] K. Menger, Géométrie Générale, Mémor. Sci. Math. no. 124, Gauthier-Villars, Paris,1954.
  • [19] D. Miheţ, On Kannan fixed point principle in generalized metric spaces, J. Nonlinear Sci. Appl. 2(2) (2009), 92–96.
  • [20] S. Bessem, A fixed point theorem in a generalized metric space for mappings satisfying a contractive condition of integral type, Int. J. Math. Anal. (Ruse) 3(25–28) (2009), 1265–1271.
  • [21] I. R. Sarma, J. M. Rao, S. S. Rao, Contractions over generalized metric spaces, J. Nonlinear Sci. Appl. 2(3) (2009), 180–182.
  • [22] B. Schweizer, A. Sklar, Statistical metric spaces, Pacific J. Math. 10 (1960), 313–334.
  • [23] B. Schweizer, A. Sklar, Probabilistic Metric Spaces, North-Holland Series in Probability and Applied Mathimatics, 5 (1983).
  • [24] A. N. Šerstnev, The triangle inequalities for random metric spaces, (Russian), Kazan. Gos. Univ. Učen. Zap. 125 (1965), 90–93.
  • [25] A. N. Šerstnev, On the probabilistic generalization of metric spaces, (Russian), Kazan. Gos. Univ. Učen. Zap. 124 (1967), 109–119.
  • [26] A. Wald, On a statistical generalization of metric spaces, Proc. Natl. Acad. Sci. U.S.A. 29 (1943), 196–197.
Uwagi
PL
Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-54a80a5e-f034-4613-87ce-1a0567a9fa66
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