Matrix characterization of oscillation for double sequences

• Autorzy: Richard Patterson , Jeff Connor , Jeannette Kline
• 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.

Słowa kluczowe

EN

double sequence; p-convergent; oscillation, double oscillations

Kategorie tematyczne

• 40A99: None of the above, but in this section
• 40A05: Convergence and divergence of series and sequences

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2008
• Tom: 6
• Numer: 3
• Strony: 488-496

Daty

wydano

2008-09-01

online

2008-07-02

Twórcy

autor

Richard Patterson

• University of North Florida

autor

Jeff Connor

• Ohio University

autor

Jeannette Kline

• Washington and Jefferson College

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

Identyfikatory

DOI

10.2478/s11533-008-0034-8