On the weighted generator of double sequences and its Tauberian conditions
Makaleler > Tam Makale · 2023
Yazarlar: Zerrin Önder, Ekrem Savaş, İbrahim ÇANAK
Advances in Operator Theory, SCI Expanded İndekslerine Giren Dergi, Uluslararası, Scopus, 2023, cilt 8
DOI: 10.1007/s43036-023-00262-0
Özet
In this paper, our aim is to make a novel interpretation of the relation between (N¯ , p, q) method and P-convergence for double sequences. In accordance with this aim, we derive some Tauberian conditions, controlling OL - and O-oscillatory behavior of the weighted generator sequence of (umn) in the sense (1, 1) relative to (Pm) and/or (Qn) , from (N¯ , p, q) summability to P-convergence with some restrictions on the weight sequences. As special cases, we indicate that OL -condition of Landau type with respect to (Pm) and (Qn) and O-condition of Hardy type with respect to (Pm) and (Qn) are Tauberian conditions for (N¯ , p, q) summability under some additional conditions. Therefore, these results contain all of the classical Tauberian theorems including slow decrease and slow oscillation conditions in certain senses.