Tbilisi Mathematical Journal

An alternative proof of the generalized Littlewood Tauberian theorem for Cesàro summable double sequences

Gökşen Findik, İbrahim Çanak, and Ümit Totur

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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.

Article information

Source
Tbilisi Math. J., Volume 12, Issue 1 (2019), 131-148.

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

Permanent link to this document
https://projecteuclid.org/euclid.tbilisi/1553565632

Digital Object Identifier
doi:10.32513/tbilisi/1553565632

Mathematical Reviews number (MathSciNet)
MR3954225

Subjects
Primary: 40E05: Tauberian theorems, general
Secondary: 40G05: Cesàro, Euler, Nörlund and Hausdorff methods

Keywords
Tauberian conditions and theorems convergence in Pringsheim's sense slow oscillation double sequences summability $(C,1,0)$, $(C,0,1)$ and $(C,1,1)$

Citation

Findik, Gökşen; Çanak, İbrahim; Totur, Ümit. An alternative proof of the generalized Littlewood Tauberian theorem for Cesàro summable double sequences. Tbilisi Math. J. 12 (2019), no. 1, 131--148. doi:10.32513/tbilisi/1553565632. https://projecteuclid.org/euclid.tbilisi/1553565632


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