THE NOVEL TAUBERIAN CONDITIONS ASSOCIATED WITH THE (N,PQ) SUMMABILITY OF DOUBLE SEQUENCES

Önder Şentürk Z., SAVAŞ E., ÇANAK İ.

Journal of Nonlinear and Convex Analysis, cilt.25, sa.9, ss.2317-2335, 2024 (SCI-Expanded) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 25 Sayı: 9
  • Basım Tarihi: 2024
  • Dergi Adı: Journal of Nonlinear and Convex Analysis
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet, zbMATH
  • Sayfa Sayıları: ss.2317-2335
  • Anahtar Kelimeler: (N, p, q) summability, convergence in Pringsheim's sense, Double sequences, regularly varying sequences, slowly decreasing sequences, slowly oscillating sequences, Tauberian conditions and theorems, weighted mean summability method
  • Uşak Üniversitesi Adresli: Evet

Özet

In this paper, our primary objective is to provide a fresh perspective on the relationship between the (N,pq) method, which is a product of relevant one-dimensional summability methods, and P-convergence for double sequences. To accomplish this objective, we establish certain Tauberian conditions that control the behavior of a double sequence in terms of both Oz,-oscillation and O-oscillation in certain senses, building a bridge between (N,pq) summability and P-convergence, while imposing certain restrictions on the weight sequences. As special circumstances of our findings, we demonstrate that Landau-type Ol condition with respect to (Pm) and (Qn), as well as Hardy-type O condition with respect to (Pm) and (Qn), serve as Tauberian conditions for (N,pq) summability under particular additional conditions. Consequently, these results encompass all classical Tauberian theorems, including conditions such as slow decrease or slow oscillation in certain senses.