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Acta Mathematica Hungarica
Volume/Issue:
Volume 102: Issue 4
DOI:
https://doi.org/10.1023/b:amhu.0000024678.80514.94
Authors:
Ferenc Móricz
and
B. Rhoades

Abstract  

We prove [1, Theorems 1 and 2] under weaker conditions and in a simpler way than we did in the cited paper.

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Acta Mathematica Hungarica
Volume/Issue:
Volume 129: Issue 1-2
DOI:
https://doi.org/10.1007/s10474-010-9256-x
Authors:
R. Patterson
and
B. Rhoades

Abstract  

In 1930 Knopp presented the following matrix characterization for the core of ordinary sequences. If A is a nonnegative regular matrix then the core of [Ax] is contained in the core of [x], provided that [Ax] exists. Patterson in 1999 extended Knopp’s results to double sequences via four dimensional matrices. In a manner similar to the Knopp’s and Patterson’s results we present multidimensional extensions of Bustoz’s singular dimensional Gibbs phenomenon results. These results include a notion of what it means for a four dimensional matrix transformation to induce the double Gibbs phenomenon in s. In addition, necessary and sufficient conditions for a four dimensional matrix to induce the double Gibbs phenomenon is also presented.

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Periodica Mathematica Hungarica
Volume/Issue:
Volume 62: Issue 2
DOI:
https://doi.org/10.1007/s10998-011-6121-9
Authors:
Ekrem Savaş
and
B. Rhoades

Abstract  

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

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Analysis Mathematica
Volume/Issue:
Volume 35: Issue 4
DOI:
https://doi.org/10.1007/s10476-009-0401-0
Authors:
Ekrem Savaş
and
B. Rhoades

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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Acta Mathematica Hungarica
Volume/Issue:
Volume 112: Issue 1-2
DOI:
https://doi.org/10.1007/s10474-006-0061-5
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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Periodica Mathematica Hungarica
Volume/Issue:
Volume 51: Issue 1
DOI:
https://doi.org/10.1007/s10998-005-0020-x
Authors:
B. E. Rhoades
and
Ekrem Savaş

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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Acta Mathematica Hungarica
Volume/Issue:
Volume 66: Issue 1-2
DOI:
https://doi.org/10.1007/bf01874356
Authors:
F. Móricz
and
B. E. Rhoades
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