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Tytuł artykułu

Implicit functions under fixed point consideration in Probabilistic Menger Spaces

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Języki publikacji
EN
Abstrakty
EN
In the present paper, we have introduced a pair of weakly-biased maps in the Probabilistic Menger Spaces under the implicit relation. Our results proved herein is the partial extension and mild improvement of the results due to Imdad, Tanveer and Hasan [10]. We have discussed an example in support of our main theorem.
Rocznik
Tom
Strony
45--61
Opis fizyczny
Bibliogr. 21 poz.
Twórcy
autor
  • Department of Pure and Applied Mathematics
  • Department of Pure and Applied Mathematics
autor
  • Department of Pure and Applied Mathematics
Bibliografia
  • [1] Schweizer B., Sklar A., Probabilistic Metric Spaces, North-Holland Series in Probability and Applied Mathimatics, 5(1983).
  • [2] Patel D.K., Kumam P., Gopal D., Some discussion on the existence of common fixed points for a pair of maps, Fixed point theory and applications, 187(2013).
  • 13] Gopal D., Abbas M., Vetro C., Some new fixed point theorems in Menger PM-spaces with applications to Volterra type integral equation, Applied Mathematics Computation, 232(2014), 955-967.
  • [4] Jungck G., Commuting Mappings And Fixed Points, American Mathematical Monthly, 83(1976), 261-263.
  • [5] Jungck G., Rhoades B.E., Fixed points for set valued functions without continuity, Indian Journal Pure Applied Mathematics, 29(3)(1998), 227-238.
  • [6] Jungck G., Pathak H.K., Fixed Points via ‘biased maps, Proceedings of the American Mathematical Society, 123(1995), 2049-2060.
  • [7] Jungck G., Common fixed points of non-metric spaces, Far East Journal of mathematical Science, 4(2)(1996), 199-215.
  • [8] Menger K., Statistical metrics, Proceedings of the National Academy of Science USA, 28(12)(1942), 535-537.
  • [9] Aamri M., El Moutawaki D., Some new common fixed point theorems under strict contractive conditions, Journal of Mathematocal Analysis and Application, 270(2002), 181-188.
  • [10] Imdad M., M.Tanveer M., Hasan M., Some common fixed point theorems in Menger PM space, Fixed Point Theory and Applications, Volume 2010, Article ID 819269, 14 pages.
  • [11] Tanveer M., Imdad M., Gopal D., Patel D.K., Common fixed point theorems in modified intuitionistic fuzzy metric spaces with common property (E.A), Fixed Point Theory and Applications, 2012(2012), 36.
  • [12] Murthy P.P., Singh M.R., Singh L.S., Weakly biased maps as a generalization of occasionally weakly compatible maps, International Journal of Pure and Applied Mathematics, (2014), 143-153.
  • [13] Sessa S., On a weak commutativity condition of mappings in fixed point considerations, Publications Del’llnstitut Mathematique (Beograd) (N.S.), 32 (46)(1982), 149-153.
  • [14] Beloul S., A common fixed point theorem for weakly subsequentially sontin-uous mappings satisfying implicit relation in Menger space, Facta Universitis, 5(2015),719-729.
  • [15] Mishra S.N., Common fixed points of compatible mappings in probabilistic metric spaces, Mathamatica Japonica, 36(1991), 283-289.
  • [16] Kumar S., Rani A., Some common fixed point theorems in Menger space, Applied Mathamatics, 3(2012), 235-245.
  • [17] Doenovi T., Kumam P., Gopal D., Patel D.K., Takai A., On fixed point theorems involving altering distances in Menger probabilistic metric spaces, Journal of Ineqqualities and Application, (2013), 567.
  • [18] Sehgal V.M., Bharucha-Reid A.T., Fixed points of contraction mappings on probabilistic metric spaces, Proceedings of the American Mathematical Society, 13(1972), 97-102.
  • [19] Popa V., A General Fixed Point Theorem for Weakly Compatible Mappings in Compact Metric Spaces, Turkish J. Math., 25(2)(2015), 465-474.
  • [20] Lie Y., Ali J., Khan L., Coincidence and fixed points in symmetric spaces under strict contractions, Journal of Mathematical Anaiysis and Application, 32(2008), 117-124.
  • [21] Cho Y.J., Murthy P.P., Stojakovic M., Compatible mappings of type (A) and common fixed point in Menger spaces, Communications of the Korean Mathematical Society, 7(2), 325-339.
Uwagi
Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2021).
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-7743a18b-e16b-4737-8c92-dd26e28351e8
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