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Modes of (α)-convergence of sequences of functions

Identyfikatory
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
In this paper we deal with continuous convergence and some related properties of sequences of functions. We present some conditions to get uniform convergence of the sequence involved to a constant function. As an application, we give a result on equivalence between modes of convergence.
Rocznik
Strony
83--94
Opis fizyczny
Bibliogr. 18 poz.
Twórcy
  • Department of Mathematics, University of Athens Panepistimiopolis, Athens 15784, Greece
autor
  • Department of Mathematics and Computer Sciences, University of Perugia via Vanvitelli 1, I-06123 Perugia, Italy
  • Department of Mathematics, University of Athens Panepistimiopolis, Athens 15784, Greece
Bibliografia
  • [1] E. Athanassiadou, A. Boccuto, X. Dimitriou and N. Papanastassiou, Ascoli-type theorems and ideal _-convergence, Filomat 26 (2) (2012), 397-405.
  • [2] A. Boccuto and D. Candeloro, Integral and ideals in Riesz spaces, Inform. Sci. 179 (2009), 647-660.
  • [3] A. Boccuto, X. Dimitriou and N. Papanastassiou, Modes of continuity involving almost and ideal convergence, Tatra Mt. Math. Publ. 52 (2012), 115-131. doi:10.2478/v10127-012-0032-x
  • [4] A. Boccuto, X. Dimitriou, N. Papanastassiou and W. Wilczynski, Ideal exhaustiveness, continuity and (α)-convergence for lattice group-valued functions, Int. J. Pure Appl. Math. 70 (2) (2011), 211-227.
  • [5] A. Boccuto and A. R. Sambucini, Abstract convergence in convergence groups, Atti Semin. Mat. Fis. Univ. Modena 46 (1998), 315-333.
  • [6] C. Carathéodory, Stetige Konvergenz und normale Familien von Funktionen, Math. Ann. 101 (1929), 515-533.
  • [7] J. Connor and K. G. Grosse-Erdmann, Sequential definitions of continuity for real functions, Rocky Mountain J. Math. 33 (1) (2003), 93-121.
  • [8] H. Fast, Sur la convergence statistique, Colloq. Math. 2 (1951), 41-44.
  • [9] G. G. Lorentz, A contribution to the theory of divergent sequences, Acta Math. 80 (1948), 167-190.
  • [10] V. Gregoriades and N. Papanastassiou, The notion of exhaustiveness and Ascoli-type theorems, Topology Appl. 155 (2008), 1111-1128.
  • [11] H. Hahn, Theorie der Reellen Funktionen, Springer, Berlin, 1921.
  • [12] E. Kolk, Inclusion relations between the statistical convergence and strong summability, Acta Comment. Univ. Tartu. Math. 2 (1998), 39-54.
  • [13] P. Kostyrko, T. ˇSalát and W. Wilczynski, I-convergence, Real Anal. Exchange 26 (2000/2001), 669-685.
  • [14] K. Kuratowski, Topology, Volls. I and II, Academic Press, New York-London, 1966/1968.
  • [15] J. Novak, On Convergence spaces and their sequential envelopes, Czech. Math. J. 15 (1) (1965), 74-100.
  • [16] Ch. Papachristodoulos, N. Papanastassiou and W. Wilczynski, I-exhaustive sequences of functions, Selected papers of the ICTA 2010 (2012).
  • [17] J. Pochciał , Sequential characterizations of metrizability, Czech. Math. J. 41 (2) (1991), 203-215.
  • [18] H. Steinhaus, Sur la convergence ordinaire et la convergence asymptotique, Colloq. Math. 2 (1951), 73-74.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-f70ba5a5-9767-4b96-b200-507dc4e1c924
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