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January 2019 An alternative proof of the generalized Littlewood Tauberian theorem for Cesàro summable double sequences
Gökşen Findik, İbrahim Çanak, Ümit Totur
Tbilisi Math. J. 12(1): 131-148 (January 2019). DOI: 10.32513/tbilisi/1553565632

Abstract

In this paper, we first examine the relationships between a double sequence and its arithmetic means in different senses (i. e. $(C,1,0)$, $(C,0,1)$ and $(C,1,1)$ means) in terms of slow oscillation in certain senses and investigate some properties of oscillatory behaviors of the difference sequence between the double sequence and its arithmetic means in different senses. Next, we give an alternative proof of the generalized Littlewood Tauberian theorem for Cesàro summability method as an application of the results obtained in the first part.

Citation

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Gökşen Findik. İbrahim Çanak. Ümit Totur. "An alternative proof of the generalized Littlewood Tauberian theorem for Cesàro summable double sequences." Tbilisi Math. J. 12 (1) 131 - 148, January 2019. https://doi.org/10.32513/tbilisi/1553565632

Information

Received: 21 March 2018; Accepted: 25 January 2019; Published: January 2019
First available in Project Euclid: 26 March 2019

zbMATH: 07172306
MathSciNet: MR3954225
Digital Object Identifier: 10.32513/tbilisi/1553565632

Subjects:
Primary: 40E05
Secondary: 40G05

Rights: Copyright © 2019 Tbilisi Centre for Mathematical Sciences

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Vol.12 • No. 1 • January 2019
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