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1
Content available remote New properties of the Natarajan method of summability
Natarajan P. N.
Commentationes Mathematicae
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2015
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Vol 55, No. 1
9--15
EN
The M; λn method of summability was introduced in 2013 by Natarajan. In the paper some new properties of this method are studied.
2
Content available remote The Schur and Steinhaus Theorems for 4-Dimensional Infinite Matrices
Natarajan P. N.
Commentationes Mathematicae
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2014
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Vol 54, No. 2
159--165
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.
3
Content available remote Steinhaus Type Theorems for (c,1) Summable Sequences
Natarajan P. N.
Commentationes Mathematicae
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2014
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Vol 54, No. 1
21--27
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.
4
Content available remote A Tauberian Theorem for Weighted Means in Non-Archimedean Fields - Revisited and Revised
Natarajan P. N.
Commentationes Mathematicae
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2014
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Vol 54, No. 2
177--178
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].
5
Content available remote A New Definition of Convergence of a Double Sequence and a Double Series and Silverman-Toeplitz Theorem
Natarajan P. N.
Commentationes Mathematicae
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2014
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Vol 54, No. 1
129--139
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.
6
Content available remote Cauchy multiplication of Euler summable series in ultrametric fields
Deepa R., Natarajan P. N., Srinivasan V.
Commentationes Mathematicae
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2013
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Vol 53, No. 1
73--79
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.
7
Content available remote An addendum to the paper “Some characterizations of Schur matrices in ultrametric fields”
Natarajan P. N.
Commentationes Mathematicae
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2013
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Vol 53, No. 1
81--82
EN
In this short note, we add a few remarks in the context of [1].
8
Content available remote Some characterizations of Schur matrices in ultrametric fields
Natarajan P.N.
Commentationes Mathematicae
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2012
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Vol. 52, [Z] 2
137--142
EN
In this short paper, K denotes a complete, non-trivially valued, ultra-metric 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.
9
Content available remote A Generalization of a Theorem of Móricz and Rhoades on Weighted Means
Natarajan P.N.
Commentationes Mathematicae
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2012
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Vol. 52, [Z] 1
29-37
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 Pn/Pn→ 0 as n→∞.
10
Content available remote The Schur and Steinhaus Theorems for 4-Dimensional Matrices in Ultrametric Fields
Natarajan P.N.
Commentationes Mathematicae
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2011
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Vol. 51, [Z] 2
203-209
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.
11
Content available remote Another Theorem on Weighted Means
Natarajan P.N.
Commentationes Mathematicae
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2010
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Vol. 50, [Z] 2
175-181
EN
In this short paper, which is a continuation of [2], we prove another interesting result concerning weighted means.
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