A New Definition of Convergence of a Double Sequence and a Double Series and Silverman-Toeplitz Theorem

• Autorzy: Natarajan P. N.

Identyfikatory

DOI

10.14708/cm.v54i1.766

• Języki publikacji: EN

Abstrakty

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.

Słowa kluczowe

EN

convergence of a double sequence and a double series; regularity of 4-dimensional infinite matrices; Silverman-Toeplitz theorem for double sequences and double series

• Wydawca: Polskie Towarzystwo Matematyczne
• Czasopismo: Commentationes Mathematicae
• Rocznik: 2014
• Tom: Vol 54, No. 1
• Strony: 129--139
• Opis fizyczny: Bibliogr. 3 poz.

Twórcy

autor

Natarajan P. N.

• Old No. 2/3, New No. 3/3 Second Main Road, R.A. Puram, Chennai 600 028, India

Bibliografia

• [1] Kojima, On the theory of double sequences, Tˆohoku Math. J. 21 (1922), 3–14.
• [2] P.N. Natarajan and V. Srinivasan, Silverman-Toeplitz theorem for double sequences and series and its application to Nörlund means in non-archimedean fields, Ann. Math. Blaise Pascal 9 (2002), 85–100.
• [3] G.M. Robison, Divergent double sequences and series, Trans. Amer. Math. Soc. 28 (1926), 50–73.