Ideal convergence generated by double summability methods

Connor, J.

Artykuł - szczegóły

Tytuł artykułu

Ideal convergence generated by double summability methods

Autorzy

Connor J.

Wybrane pełne teksty z tego czasopisma

http://www.degruyter.com/view/j/dema

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Warianty tytułu

Języki publikacji

Abstrakty

The main result of this note is that if I is an ideal generated by a regular double summability matrix summability method T that is the product of two nonnegative regular matrix methods for single sequences, then I-statistical convergence and convergence in I-density are equivalent. In particular, the method T generates a density μT with the additive property (AP) and hence, the additive property for null sets (APO). The densities used to generate statistical convergence, lacunary statistical convergence, and general de la Vallée-Poussin statistical convergence are generated by these types of double summability methods. If a matrix T generates a density with the additive property then T-statistical convergence, convergence in T-density and strong T-summabilty are equivalent for bounded sequences. An example is given to show that not every regular double summability matrix generates a density with additve property for null sets.

Słowa kluczowe

ideal convergence statistical convergence double summability methods densities additive property

zbieżność idealna zbieżność statystyczna gęstość właściwość addytywna

Wydawca

De Gruyter

Czasopismo

Demonstratio Mathematica

Rocznik

2016

Tom

Vol. 49, nr 1

Strony

26--37

Opis fizyczny

Bibliogr. 24 poz.

Twórcy

autor

Connor J.

connorj@ohio.edu

Department of Mathematics Ohio University Athens, Ohio 45701, U.S.A.

Bibliografia

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[6] J. Connor, M. A. Swardson, Strong integral summability and the Stone-Čech compactification of the half-line, Pacific J. Math. 157(2) (1993), 201–224.
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[19] R. F. Patterson, E. Savaş, Lacunary statistical convergence of double sequences, Math. Commun. 10(1) (2005), 55–61.
[20] G. M. Petersen, Regular Matrix Transformations, McGraw-Hill Publishing Co., Ltd., London-New York-Toronto, Ont., 1966.
[21] R. E. Powell, S. M. Shah, Summability Theory and Applications, Van Nostrand Reinhold, 1972.
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[24] B. Ch. Tripathy, Statistically convergent double sequences, Tamkang J. Math. 34(3) (2003), 231–237.

Uwagi

Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę.

Typ dokumentu

Bibliografia

Identyfikator YADDA

bwmeta1.element.baztech-07494782-f5f4-4efd-88e0-112d05ead6e9