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2008 | 6 | 3 | 488-496
Tytuł artykułu

Matrix characterization of oscillation for double sequences

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
The notion of oscillation for ordinary sequences was presented by Hurwitz in 1930. Using this notion Agnew and Hurwitz presented regular matrix characterization of the resulting sequence space. The primary goal of this article is to extend this definition to double sequences, which grants us the following definition: the double oscillation of a double sequence of real or complex number is given P-lim sup(m,n)→∞;(α,β)→∞|S m,n-S α,β|. Using this concept a matrix characterization of double oscillation sequence space is presented. Other implication and variation shall also be presented.
Wydawca
Czasopismo
Rocznik
Tom
6
Numer
3
Strony
488-496
Opis fizyczny
Daty
wydano
2008-09-01
online
2008-07-02
Twórcy
autor
Bibliografia
  • [1] Agnew R.P., The effects of general regular transformations on oscillations of sequences of functions, Trans. Amer. Math. Soc., 1931, 33, 411–424 http://dx.doi.org/10.2307/1989412
  • [2] Hamilton H.J., Transformations of multiple sequences, Duke Math. J., 1936, 2, 29–60 http://dx.doi.org/10.1215/S0012-7094-36-00204-1
  • [3] Hurwitz W.A., The oscillation of a sequence, Amer. J. Math., 1930, 52, 611–616 http://dx.doi.org/10.2307/2370629
  • [4] Mursaleen, Edely O.H., Statistical convergence of double sequences, J. Math. Anal. Appl., 2003, 288, 223–231 http://dx.doi.org/10.1016/j.jmaa.2003.08.004
  • [5] Patterson R.F., Analogues of some fundamental theorems of summability theory, Int. J. Math. Math. Sci., 2000, 23, 1–9 http://dx.doi.org/10.1155/S0161171200001782
  • [6] Pringsheim A., Zur theorie der zweifach unendlichen Zahlenfolgen, Math. Ann., 1900, 53, 289–321 (in German) http://dx.doi.org/10.1007/BF01448977
  • [7] Robison G.M., Divergent double sequences and series, Trans. Amer. Math. Soc., 1926, 28, 50–73 http://dx.doi.org/10.2307/1989172
  • [8] Savas E., On some new double sequence spaces defined by a modulus, Appl. Math. Comput, 2007, 187, 417–424 http://dx.doi.org/10.1016/j.amc.2006.08.141
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_2478_s11533-008-0034-8
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