Abstract
In this paper, we obtain necessary and sufficient conditions, under which convergence of a double sequence in Pringsheim's sense follows from its weighted-Cesaro summability. These Tauberian conditions are one-sided or two-sided if it is a sequence of real or complex numbers, respectively.
Publisher
Sociedade Paranaense de Matematica
Reference11 articles.
1. 1. Baron, S., Stadtmuller, U., Tauberian theorems for power series methods applied to double sequences, J. Math. Anal. Appl. 211, 574-589, (1997).
2. 2. Braha, N. L., Some weighted equi-statistical convergence and Korovkin type-theorem, Results Math. 70(3-4), 433-446, (2016).
3. 3. Chen, C., Hsu, J., Tauberian theorems for weighted means of double sequences, Anal. Math. 26(4), 243-262, (2000).
4. 4. Fındık, G., Canak, I., Tauberian theorems for the product of weighted and Cesaro summability methods for double sequences, In Cakalli, H., Deger, O. (Eds.), Abstract book. Paper presented at the 2nd International Conference of Mathematical Sciences (ICMS 2018), Maltepe University, Istanbul, Turkey, July 31–August 6, 2018 (p. 89).
5. 5. Knopp, K., Limitierungs-Umkehrsatze fur Doppelfolgen, Math. Z. 45, 573-589, (1939).