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Rough I-convergence

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Języki publikacji
EN
Abstrakty
EN
In this work, using the concept of I-convergence and using the concept of rough convergence, we introduced the notion of rough I-convergence and the set of rough I-limit points of a sequence and obtained two rough I-convergence criteria associated with this set. Later, we proved that this set is closed and convex. Finally, we examined the relations between the set of I-cluster points and the set of rough I-limit points of a sequence.
Wydawca
Rocznik
Strony
638--651
Opis fizyczny
Bibliogr. 15 poz.
Twórcy
autor
  • Department of Mathematics, Afyon Kocatepe University, 0320-Afyonkarahisar, Turkey
autor
  • Inönü University, Faculty of Education, 44280-Malatya, Turkey
Bibliografia
  • [1] S. Aytar, Rough statistical convergence, Numer. Funct. Anal. Optim. 29(3-4) (2008), 291–303.
  • [2] S. Aytar, The rough limit set and the core of a real requence, Numer. Funct. Anal. Optim. 29(3-4) (2008), 283–290.
  • [3] K. Demirci, I-limit superior and limit inferior, Math. Commun. 6 (2001), 165–172.
  • [4] H. Fast, Sur la convergenc statistique, Colloq. Math. 2 (1951), 241–244.
  • [5] J. A. Fridy, On statistical convergence, Analysis 5 (1985), 301–313.
  • [6] P. Kostyrko, T. Salat, W. Wilczynski, I-convergence, Real Anal. Exchange 26(2) (2000), 669–686.
  • [7] P. Kostyrko, M. Macaj, T. Salat, M. Sleziak, I-convergence and extremal I-limit points, Math. Slovaca 55 (2005), 443–464.
  • [8] H. I. Miller, A measure theoretical subsequence characterization of statistical convergence, Trans. Amer. Math. Soc. 347 (1995), 1811–1819.
  • [9] F. Nuray, W. H. Ruckle, Generalized statistical convergence and convergence free spaces, J. Math. Anal. Appl. 245 (2000), 513–527.
  • [10] H. X. Phu, Rough convergence in normed linear spaces, Numer. Funct. Anal. Optim. 22 (2001), 199–222.
  • [11] H. X. Phu, Rough continuity of linear operators, Numer. Funct. Anal. Optim. 23 (2002), 139–146.
  • [12] H. X. Phu, Rough convergence in infinite dimensional normed spaces, Numer. Funct. Anal. Optim. 24 (2003), 285–301.
  • [13] T. Šalát, B. C. Tripathy, M. Ziman, On I-convergence field, Ital. J. Pure Appl. Math. 17 (2005), 45–54.
  • [14] T. Šalát, On statistically convergent sequences of real numbers, Math. Slovaca 30 (1980), 139–150.
  • [15] I. J. Schoenberg, The integrability of certain functions and related summability methods, Amer. Math. Monthly 66 (1959), 361–375.
Typ dokumentu
Bibliografia
Identyfikator YADDA
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