On Some Analytical Relations Between Double Summability Methods of Abel-Natarajan

Josef Al

doi:https://doi.org/10.54216/GJMSA.060203

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Volume 6 • Issue 2 • PP: 29-31 • 2023

On Some Analytical Relations Between Double Summability Methods of Abel-Natarajan

Josef Al Jumayel ^1*

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¹Faculty Of Science, Beirut Arab University, Beirut, Lebanon

* Corresponding Author.

DOI https://doi.org/10.54216/GJMSA.060203

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Received: January 22, 2022 Revised: May 09, 2023 Accepted: July 08, 2023

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Abstract

This paper is dedicated to study the analytical relations between Abel's double summability method and Natarajan's double summability method, where many theorems that draw a bridge between the mentioned methods will be obtained. The main result of our work is to prove that that summability by Natarajan's method implies summability by Abel's method in one or two variables. On the other hand, we illustrate some related examples to clarify the validity of our approach.

Keywords

Natarajan's method Abel's method summability.

References

[1] P.N. Natarajan, 2016, " Natarajan method of summability for double sequences and series ", (547-552).

[2] 2. P.N. Natarajan, 2011, " Maddox's Theorems For The Natarajan Method Of Summability ", (21-26) .

[3] P.N. Natarajan, 2012, " Some Properties Of The Natarajan Method Of Summability For Double Sequences In Ultrametric Fields", (21-27).

[4] P.N. Natarajan, 2017, " Classical Summability Theory", (1-135).

[5] P.N. Natarajan, 2016, " Some Topics in Summability Theory", (1-48).

[6] P.N. Natarajan, 2016, " New Properties Of The Natarajan Method Of Summability For Double Sequences", (28-33).

[7] G. H. Hardy, 1949, " Divergent Series ", Oxford At The Clarendon Press, (65-66) .

[8] F. Başar, R. Colak, 2011, " Summability Theory and Its Applications ", Fatih University Faculty of Art and Sciences Department of Mathematics, (408).

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Jumayel, Josef Al. "On Some Analytical Relations Between Double Summability Methods of Abel-Natarajan." Galoitica: Journal of Mathematical Structures and Applications, vol. Volume 6, no. Issue 2, 2023, pp. 29-31. DOI: https://doi.org/10.54216/GJMSA.060203

Jumayel, J. (2023). On Some Analytical Relations Between Double Summability Methods of Abel-Natarajan. Galoitica: Journal of Mathematical Structures and Applications, Volume 6(Issue 2), 29-31. DOI: https://doi.org/10.54216/GJMSA.060203

Jumayel, Josef Al. "On Some Analytical Relations Between Double Summability Methods of Abel-Natarajan." Galoitica: Journal of Mathematical Structures and Applications Volume 6, no. Issue 2 (2023): 29-31. DOI: https://doi.org/10.54216/GJMSA.060203

Jumayel, J. (2023) 'On Some Analytical Relations Between Double Summability Methods of Abel-Natarajan', Galoitica: Journal of Mathematical Structures and Applications, Volume 6(Issue 2), pp. 29-31. DOI: https://doi.org/10.54216/GJMSA.060203

Jumayel J. On Some Analytical Relations Between Double Summability Methods of Abel-Natarajan. Galoitica: Journal of Mathematical Structures and Applications. 2023;Volume 6(Issue 2):29-31. DOI: https://doi.org/10.54216/GJMSA.060203

J. Jumayel, "On Some Analytical Relations Between Double Summability Methods of Abel-Natarajan," Galoitica: Journal of Mathematical Structures and Applications, vol. Volume 6, no. Issue 2, pp. 29-31, 2023. DOI: https://doi.org/10.54216/GJMSA.060203

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