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Asymptotically lacunary statistical equivalence of double sequences of sets

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Języki publikacji
EN
Abstrakty
EN
The concepts of Wijsman asymptotically equivalence, Wijsman asymptotically statistically equivalence, Wijsman asymptotically lacunary equivalence and Wijsman asymptotically lacunary statistical equivalence for sequences of sets were studied by Ulusu and Nuray [24]. In this paper, we get analogous results for double sequences of sets.
Wydawca
Rocznik
Strony
183--196
Opis fizyczny
Bibliogr. 26 poz.
Twórcy
autor
  • Deparment of Mathematics Faculty of Science and Literature Afyon Kocatepe University 03200, Afyonkarahisar, Turkey
  • Deparment of Mathematics and Statistics North Florida University Jacksonville, Fl., USA
autor
  • Deparment of Mathematics Faculty of Science and Literature Afyon Kocatepe University 03200, Afyonkarahisar, Turkey
Bibliografia
  • [1] B. Altay, F. Başar, Some new spaces of double sequences, J. Math. Anal. Appl. 309(1) (2005), 70–90.
  • [2] J.-P. Aubin, H. Frankowska, Set-valued Analysis, Birkhauser, Boston, 1990.
  • [3] M. Baronti, P. Papini, Convergence of sequences of sets, In: Methods of Functional Analysis in Approximation Theory, ISNM 76, Birkhauser-Verlag, Basel, 1986, 133–155.
  • [4] G. Beer, On convergence of closed sets in a metric space and distance functions, Bull. Austral. Math. Soc. 31 (1985), 421–432.
  • [5] G. Beer, Wijsman convergence: a survey, Set-Valued Var. Anal. 2 (1994), 77–94.
  • [6] C. Çakan, B. Altay, Statistically boundedness and statistical core of double sequences, J. Math. Anal. Appl. 317 (2006), 690–697.
  • [7] H. Fast, Sur la convergence statistique, Colloq. Math. 2 (1951), 241–244.
  • [8] J. A. Fridy, C. Orhan, Statistical limit superior and inferior, Proc. Amer. Math. Soc. 125 (1997), 3625–3631.
  • [9] J. A. Fridy, C. Orhan, Lacunary statistical convergence, Pacific J. Math. 160(1) (1993), 43–51.
  • [10] M. Marouf, Asymptotic equivalence and summability, Internat. J. Math. Sci. 16(2) (1993), 755–762.
  • [11] M. Mursaleen, O. H. H. Edely, Statistical convergence of double sequences, J. Math. Anal. Appl. 288 (2003), 223–231.
  • [12] F. Nuray, B. E. Rhoades, Statistical convergence of sequences of sets, Fasc. Math. 49 (2012), 87–99.
  • [13] F. Nuray, E. Dündar, U. Ulusu, Wijsman statistical convergence of double sequences of sets, (under communication).
  • [14] F. Nuray, U. Ulusu, E. Dündar, Wijsman lacunary statistical convergence of double sequences of sets, (under communication).
  • [15] F. Nuray, U. Ulusu, E. Dündar, Cesàro summability of double sequences of sets, (under communication).
  • [16] R. F. Patterson, On asymptotically statistically equivalent sequences, Demostratio Math. 36 (2003), 149–153.
  • [17] R. F. Patterson, E. Savaş, On asymptotically lacunary statistically equivalent sequences, Thai J. Math. 4 (2006), 267–272.
  • [18] A. Pringsheim, Zur theorie der zweifach unendlichen Zahlenfolgen, Math. Ann. 53 (1900), 289–321.
  • [19] E. Savaş, On some double lacunary sequence spaces of fuzzy numbers, Math. Comput. Appl. 15(3) (2010), 439–448.
  • [20] I. J. Schoenberg, The integrability of certain functions and related summability methods, Amer. Math. Monthly 66 (1959), 361–375.
  • [21] Y. Sever, Ö. Talo, B. Altay, On convergence of double sequence of closed sets, (under communication).
  • [22] Ö. Talo, Y. Sever, On statistically convergence of double sequence of closed sets, (under communication).
  • [23] U. Ulusu, F. Nuray, Lacunary statistical convergence of sequence of sets, Progr. Appl. Math. 4(2) (2012), 99–109.
  • [24] U. Ulusu, F. Nuray, On asymptotically lacunary statistical equivalent set sequences, J. Math., 2013, 5 pages.
  • [25] R. A. Wijsman, Convergence of sequences of convex sets, cones and functions, Bull. Amer. Math. Soc. 70 (1964), 186–188.
  • [26] R. A. Wijsman, Convergence of sequences of convex sets, cones and functions II, Trans. Amer. Math. Soc. 123(1) (1966), 32–45.
Uwagi
Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-5bfadce9-50a4-4080-9d96-d4e0f08931dc
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