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Statistical convergence of sequences of sets

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Języki publikacji
EN
Abstrakty
EN
The concept of convergence of sequences of points has been extended by several authors to convergence of sequences of sets. The three such extensions that we will consider in this paper are those of Kuratowski, Wijsman and Hausdorff. We shall define statistical convergence for sequences of sets and establish some basic theorems, thereby obtaining generalizations of the corre-sponding results for statistical convergence of sequences of points.
Słowa kluczowe
Rocznik
Tom
Strony
87--99
Opis fizyczny
Bibliog. 21 poz.
Twórcy
autor
  • Department of Mathematics Afyon Kocatepe University Afyonkarahisar, Turkey
  • Indiana University Bloomington, IN. USA
Bibliografia
  • [1] Aubin J.-P., Frankowska H., Set-Valued Analysis, Birkhauser, Boston, 1990.
  • [2] Baronti M., Papini P., Convergence of sequences of sets. In Methods of functional analysis in approximation theory, ISNM 76, Birkhauser, Basel, (1986), 133-155.
  • [3] Beer G., On the compactness theorem for Sequences of closed sets, Math. Balkanica, 16(2002), 327-338.
  • [4] Beer G., On convergence of closed sets in a metric space and distance functions, Bull. Austral. Math. Soc., 31(1985), 421-432.
  • [5] Beer G., Convergence of continuous linear functionals and their level sets, Arch. Math., 52(1989), 482-491.
  • [6] Connor J.S., The statistical and strong p-Cesaro convergence of sequences, Analysis, 8(1988), 46-63.
  • [7] Borwein J.M., Vanderwerk J., Dual Kadec-Klee norms and the relationships between Wijsman, slice and Mosco convergence, Michigan Math. J., 41(1994), 371-387.
  • [8] Fast H., Sur la convergence statistique, Colloq. Math., 2(1951), 241-244.
  • [9] Ferrera J., Convergence of polinomial level sets, Trans. Amer. Math. Soc., 350(12)(1988), 4757-4773.
  • [10] Freedman A.R., Sember J.J., Raphael M., Some Cesaro type summa- bility spaces, Proc. London Math. Soc., 37(1978), 508-520.
  • [11] Fridy J.A., On statistical convergence, Analysis, 5(1985), 301-313.
  • [12] Fridy J.A., Orhan C., Statistical limit superior and limit inferior, Proc. Amer. Math. Soc., 125(12)(1997), 3625-3631.
  • [13] Hausdorff F., Grundzugeder Mengenlehre, Verlag von Veit, Leipzig, 1914, Preprinted by Chelsea, New York.
  • [14] Kuratowski C., Topology, Vol. I, Academic Press, New York, 1966. Lorentz G.G., A contribution to the theory of divergent sequences, Acta Math., 80(1948), 167-190.
  • [15] Lorentz G.G., A contribution to the theory of divergent sequences, Acta Math., 80(1948), 167-190.
  • [16] Maddox I.J., A new type of convergence, Math. Proc. Cambridge Phil. Soc., 83(1978), 61-64.
  • [17] Schoenberg I.J., The integrability of certain functions and related summa- bility methods, Amer. Math. Monthly, 66(1959), 361-375.
  • [18] Sonntag Y., Zalinescu C., Convergences for sequences of sets and linear mappings, J. Math. Anal. and Appl., 188(1994), 616-640.
  • [19] Sonntag Y., Zalinescu C., Set convergences. An attempt of classification, Trans. Amer. Math. Soc., 340(1)(1993), 199-226.
  • [20] Wijsman R.A., Convergence of sequences of convex sets, cones and functions, Bull. Amer. Math. Soc., 70(1964), 186-188.
  • [21] Wijsman R.A., Convergence of sequences of convex sets, cones and functions II, Trans. Amer. Math. Soc., 123(1)(1966), 32-45.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-7d27241a-8749-4c92-a421-e71c9990f80d
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