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New properties of the Natarajan method of summability

Natarajan P. N.

Commentationes Mathematicae

2015

Vol 55, No. 1

9--15

The M; λn method of summability was introduced in 2013 by Natarajan. In the paper some new properties of this method are studied.

The Schur and Steinhaus Theorems for 4-Dimensional Infinite Matrices

Natarajan P. N.

Commentationes Mathematicae

2014

Vol 54, No. 2

159--165

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.

Steinhaus Type Theorems for (c,1) Summable Sequences

Natarajan P. N.

Commentationes Mathematicae

2014

Vol 54, No. 1

21--27

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.

Some characterizations of Schur matrices in ultrametric fields

Natarajan P.N.

Commentationes Mathematicae

2012

Vol. 52, [Z] 2

137--142

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.

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

Natarajan P.N.

Commentationes Mathematicae

2012

Vol. 52, [Z] 1

29-37

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→∞.

Another Theorem on Weighted Means

Natarajan P.N.

Commentationes Mathematicae

2010

Vol. 50, [Z] 2

175-181

In this short paper, which is a continuation of [2], we prove another interesting result concerning weighted means.