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1

A Generalization of a Theorem of Móricz and Rhoades on Weighted Means

100%
Natarajan P. N.
Commentationes Mathematicae
|
2012
|
tom 52
|
nr 1
EN
In this paper,we prove a theorem which gives an equivalent formulation of summability by weighted mean methods. The result of Hardy [1] and that of Móricz and Rhoades [2] are special cases of this theorem. In this context, it is important to note that the result of Móricz and Rhoades is valid even without the assumption \(\frac{p_n}{P_n}\to0\) as \(n\to\infty\).
2
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The Schur and Steinhaus Theorems for 4-Dimensional Matrices in Ultrametric Fields

100%
Natarajan P. N.
Commentationes Mathematicae
|
2011
|
tom 51
|
nr 2
EN
Throughout this paper, K denotes a ds-complete, non-trivially valued, ultrametric field. Entries of double sequences, double series and 4-dimensional matrices are in K. We prove the Schur and Steinhaus theorems for 4-dimensional matrices in such fields.
3
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An addendum to the paper "Some Characterizations of Schur Matrices in Ultrametric Fields"

100%
Natarajan P. N.
Commentationes Mathematicae
|
2013
|
tom 53
|
nr 1
EN
In this short note, we add a few remarks in the context of [1].
4
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The Schur and Steinhaus Theorems for 4-Dimensional Infinite Matrices

100%
Natarajan P. N.
Commentationes Mathematicae
|
2014
|
tom 54
|
nr 2
EN
This paper is a sequel to [2]. Throughout this paper, entries of double sequences, double series and 4-dimensional infinite matrices are real or complex numbers. We prove the Schur and Steinhaus theorems for 4-dimensional infinite matrices.
5
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A Tauberian Theorem for Weighted Means in Non-Archimedean Fields - Revisited and Revised

100%
Natarajan P. N.
Commentationes Mathematicae
|
2014
|
tom 54
|
nr 2
EN
In this note, \(K\) denotes a complete, non-trivially valued, non-archimedean field. We correct a Tauberian theorem for weighted means in \(K\) proved earlier in [1].
6
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A New Definition of Convergence of a Double Sequence and a Double Series and Silverman-Toeplitz Theorem

100%
Natarajan P. N.
Commentationes Mathematicae
|
2014
|
tom 54
|
nr 1
EN
Throughout this paper, entries of 4-dimensional infinite matrices, double sequences and double series are real or complex numbers. In the present paper, we introduce a new definition of convergence of a double sequence and a double series and record a few results on convergent double sequences. We also prove Silverman-Toeplitz theorem for double sequences and series.
7
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New properties of the Natarajan method of summability

100%
Natarajan P. N.
Commentationes Mathematicae
|
2015
|
tom 55
|
nr 1
EN
The \((M, \lambda_n)\) method of summability was introduced in 2013 by Natarajan. In the paper some new properties of this method are studied.
8
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Steinhaus Type Theorems for \((c, 1)\) Summable Sequences

100%
Natarajan P. N.
Commentationes Mathematicae
|
2014
|
tom 54
|
nr 1
EN
In this short paper, entries of infinite matrices and sequences are real or complex numbers. We prove a few Steinhaus type theorems for \((c, 1)\) summable sequences.
9
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Some Characterizations of Schur Matrices in Ultrametric Fields

100%
Natarajan P. N.
Commentationes Mathematicae
|
2012
|
tom 52
|
nr 2
EN
In this short paper, \(K\) denotes a complete, non-trivially valued, ultrametric field. Sequences and infinite matrices have entries in K. We prove a few characterizations of Schur matrices in \(K\). We then deduce some non-inclusion theorems modelled on the results of Agnew [1] and Fridy [3] in the classical case.
10
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Another Theorem on Weighted Means

100%
Natarajan P. N.
Commentationes Mathematicae
|
2010
|
tom 50
|
nr 2
EN
In this short paper, which is a continuation of [2], we prove another interesting result concerning weighted means.
11

The Steinhaus theorem for Toeplitz matrices in non-archimedean fields

88%
Natarajan P. N.
Commentationes Mathematicae
|
1978
|
tom 20
|
nr 2
EN
The article contains no abstract
12
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Cauchy Multiplication of Euler Summable Series in Ultrametric Fields

52%
Deepa R., Natarajan P. N., Srinivasan V.
Commentationes Mathematicae
|
2013
|
tom 53
|
nr 1
EN
Euler summability method in a complete, non-trivially valued, ultrametric field of the characteristic zero was introduced by Natarajan in [7]. Some properties of the Euler summability method in such fields were studied in [2] and [7]. The purpose of the present note is to continue the study and to prove a pair of theorems on the Cauchy product of Euler summable sequences and series.
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