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On asymmetric I and I∗-divergence

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Języki publikacji
EN
Abstrakty
EN
In this paper we introduce and study the concepts of I-divergence and I∗-divergence of sequences as well as double sequences in an asymmetric metric spaces. We investigate the interrelationship between I-divergence and I∗-divergence and show that they are equivalent under some condition and prove some basic properties of these concepts.
Wydawca
Rocznik
Strony
137--147
Opis fizyczny
Bibliogr. 16 poz.
Twórcy
autor
  • Department of Mathematics, Faculty of Science, Kalyani Government Engineering College, Kalyani, Nadia-741235, West Bengal, India
autor
  • Research Scholar, Department of Mathematics, Jadavpur University, Kolkata-700032, West Bengal, India
Bibliografia
  • [1] M. Balcerzak, K. Dems, A. Komisarski, Statistical convergence and ideal convergence for sequences of functions, J. Math. Anal. Appl 328(1) (2007), 715–729.
  • [2] J. Collins, J. Zimmer, An asymmetric Arzela-Ascoli theorem, Top. Appl. 154 (2007), 2312–2322.
  • [3] P. Das, S. Ghosal, S. Pal, Extending asymmetric convergence and Cauchy condition through ideals, Math. Slovaca (2011), accepted.
  • [4] P. Das, S. Ghosal, Some further results on I-Cauchy sequences and condition (AP), Comput. Math. Appl. 59 (2010), 2597–2600.
  • [5] P. Das, P. Kostyrko, W. Wilczyński, P. Malik, I and I∗-convergence of double sequences, Math. Slovaca 58(5) (2008), 605–620.
  • [6] H. Fast, Sur la convergence statistique, Colloq. Math. 2 (1951), 241–244.
  • [7] J. A. Fridy, On statistical convergence, Analysis 5 (1985), 301–313.
  • [8] H. P. A. Kunzi, A note on sequentially compact quasipseudometric spaces, Monatsh. Math. 95(3) (1983), 219–220.
  • [9] M. Katetov, Products of filters, Comment. Math. Univ. Carolin. 9 (1968), 173–189.
  • [10] P. Kostyrko, T. Šalát, W. Wilczyński, I-convergence, Real Anal. Exchange 26(2) (2000/2001), 669–685.
  • [11] A. Mennucci, On asymmetric distances, Technical report, Scuola Normale Superiore, Pisa, 2004.
  • [12] M. Macaj, T. Šalát, Statistical convergence of subsequences of a given sequence, Math. Bohem. 126 (2001), 191–208.
  • [13] A. Nabiev, S. Pehlivan, M. Gurdal, On I-Cauchy sequences, Taiwanese J. Math. 11(2) (2007), 569–576.
  • [14] T. Šalát, On statistically convergent sequences of real numbers, Math. Slovaca 30 (1980), 139–150.
  • [15] H. Steinhaus, Sur la convergence ordinaire et la convergence asymptotique, Colloq. Math. 2 (1951), 73–74.
  • [16] W. A. Wilson, On quasi-metric spaces, Amer. J. Math. 53(3) (1991), 675–684.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-7730127a-374e-4bf9-99e9-8a79908e9a32
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