Matrix characterization of oscillation for double sequences
Richard Patterson; Jeff Connor; Jeannette Kline
Open Mathematics (2008)
- Volume: 6, Issue: 3, page 488-496
- ISSN: 2391-5455
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topRichard Patterson, Jeff Connor, and Jeannette Kline. "Matrix characterization of oscillation for double sequences." Open Mathematics 6.3 (2008): 488-496. <http://eudml.org/doc/269522>.
@article{RichardPatterson2008,
abstract = {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.},
author = {Richard Patterson, Jeff Connor, Jeannette Kline},
journal = {Open Mathematics},
keywords = {double sequence; p-convergent; oscillation, double oscillations; -convergent; double oscillations},
language = {eng},
number = {3},
pages = {488-496},
title = {Matrix characterization of oscillation for double sequences},
url = {http://eudml.org/doc/269522},
volume = {6},
year = {2008},
}
TY - JOUR
AU - Richard Patterson
AU - Jeff Connor
AU - Jeannette Kline
TI - Matrix characterization of oscillation for double sequences
JO - Open Mathematics
PY - 2008
VL - 6
IS - 3
SP - 488
EP - 496
AB - 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.
LA - eng
KW - double sequence; p-convergent; oscillation, double oscillations; -convergent; double oscillations
UR - http://eudml.org/doc/269522
ER -
References
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- [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 Zbl0954.40005
- [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 Zbl52.0223.01
- [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 Zbl1126.46300
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