An alternative proof of the generalized Littlewood Tauberian theorem for Cesàro summable double sequences
Articles > Article · 2019
Authors: İbrahim ÇANAK, Ibrahim Canak, Umit Totur
Tbilisi Mathematical Journal, Journal Indexed in SCI Expanded, International, WoS, 2019, vol 12, pp 131-148
DOI: 10.32513/tbilisi/1553565632
Summary
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.