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Galoitica: Journal of Mathematical Structures and Applications

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Galoitica: Journal of Mathematical Structures and Applications

Volume 6 , Issue 2 , PP: 29-31, 2023 | Cite this article as | XML | Html | PDF

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

Josef Al Jumayel 1 *

  • 1 Faculty Of Science, Beirut Arab University, Beirut, Lebanon - (Josefjumayel113@gmail.com)

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

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

    Cite This Article As :
    Josef Al Jumayel. "On Some Analytical Relations Between Double Summability Methods of Abel-Natarajan." Full Length Article, Vol. 6, No. 2, 2023 ,PP. 29-31 (Doi   :  https://doi.org/10.54216/GJMSA.060203)
    Josef Al Jumayel. (2023). On Some Analytical Relations Between Double Summability Methods of Abel-Natarajan. Journal of , 6 ( 2 ), 29-31 (Doi   :  https://doi.org/10.54216/GJMSA.060203)
    Josef Al Jumayel. "On Some Analytical Relations Between Double Summability Methods of Abel-Natarajan." Journal of , 6 no. 2 (2023): 29-31 (Doi   :  https://doi.org/10.54216/GJMSA.060203)
    Josef Al Jumayel. (2023). On Some Analytical Relations Between Double Summability Methods of Abel-Natarajan. Journal of , 6 ( 2 ), 29-31 (Doi   :  https://doi.org/10.54216/GJMSA.060203)
    Josef Al Jumayel. On Some Analytical Relations Between Double Summability Methods of Abel-Natarajan. Journal of , (2023); 6 ( 2 ): 29-31 (Doi   :  https://doi.org/10.54216/GJMSA.060203)
    Josef Al Jumayel, On Some Analytical Relations Between Double Summability Methods of Abel-Natarajan, Journal of , Vol. 6 , No. 2 , (2023) : 29-31 (Doi   :  https://doi.org/10.54216/GJMSA.060203)

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