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1
Content available Some Characterizations of Schur Matrices in Ultrametric Fields
100%
Natarajan P. N.
Commentationes Mathematicae
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2012
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tom 52
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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.
2
Content available The Schur and Steinhaus Theorems for 4-Dimensional Infinite Matrices
100%
Natarajan P. N.
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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.
3
Content available remote Some characterizations of Schur matrices in ultrametric fields
100%
Natarajan P. N.
Commentationes Mathematicae
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2012
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tom 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.
4
Content available remote The Schur and Steinhaus Theorems for 4-Dimensional Infinite Matrices
86%
Natarajan P. N.
Commentationes Mathematicae
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2014
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tom 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.
5
Content available The Schur and Steinhaus Theorems for 4-Dimensional Matrices in Ultrametric Fields
86%
Natarajan P. N.
Commentationes Mathematicae
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2011
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tom 51
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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.
6
Content available remote The Schur and Steinhaus Theorems for 4-Dimensional Matrices in Ultrametric Fields
86%
Natarajan P. N.
Commentationes Mathematicae
|
2011
|
tom 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.
7
Results of Tadeusz Świątkowski on algebraic sums of sets and their applications in the theory of subadditive functions
58%
Matkowski J.
Journal of Applied Analysis
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2012
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tom Vol. 18, nr 1
97-116
EN
A refinement of Steinhaus' theorem on the algebraic sum of subsets of R due to Raikov (1939) was not known to the mathematical community and still is not popular. In 1994, Tadeusz Świątkowski, being not aware of the existence of Raikov's theorem, proved another result of this type. Unfortunately, a few days later he passed away. In this paper we present the theorems of Świątkowski and Raikov and we apply them in the theory of subadditive type inequalities. An improvement of a converse of Minkowski's inequality theorem is presented.
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