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  • Author or Editor: Ekrem Savaş x
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Authors: Richard Patterson and Ekrem Savaş

In 1945 Brudno presented the following important theorem: If A and B are regular summability matrix methods such that every bounded sequence summed by A is also summed by B , then it is summed by B to the same value. In 1960 Petersen extended Brudno’s theorem by using uniformly summable methods. The goal of this paper is to extend Petersen’s theorem to double sequences by using four dimensional matrix transformations and notion of uniformly summable methods for double sequences. In addition to this extension we shall also present an accessible analogue of this theorem.

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In 1936 Hamilton presented a Silverman-Toeplitz type characterization of c0 (i.e. the space of bounded double Pringsheim null sequences). In this paper we begin with the presentation of a notion of asymptotically statistical regular. Using this definition and the concept of maximum remaining difference for double sequence, we present the following Silverman-Toeplitz type characterization of double statistical rate of convergence: let A be a nonnegative c0c0 summability matrix and let [x] and [y] be member of l″ such that with [x] ∈ P 0, and [y] ∈ P δ for some δ > 0 then µ(Ax) µ(Ay). In addition other implications and variations shall also be presented.

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We introduce the concept of double uniform density of subsets of ℕ×ℕ and the study the corresponding convergence (namely, I u-convergence) of double sequences. Further we solve an inequality related to the I u-limit superior of bounded double sequences in line of [5].

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Abstract  

We obtain necessary conditions for a doubly triangular matrix A to have the property that a double series ΣΣ λmn b mn is summable |A|k whenever the series ΣΣb mn is bounded |A|k.

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Abstract  

Let A denote the set of kth absolutely summable double series. In this paper it is shown that every double conservative Hausdorff matrix is a bounded operator on A.

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Authors: B. E. Rhoades and Ekrem Savaş

Summary  

The paper deals with absolute summability factors for infinite series. The main result obtained in this paper generalizes a recent paper of Mazhar.

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Summary  

We obtain sufficient conditions for the series \documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $\sum a_{n}\lambda_{n}$ \end{document} to be absolutely summable of order \documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $k$ \end{document} by atriangular matrix.

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