Some novel approaches on the (N, p, q) summability of double sequences of fuzzy numbers and its applications

Önder Şentürk Z., SAVAŞ E., ÇANAK İ.

Iranian Journal of Fuzzy Systems, cilt.20, sa.6, ss.105-122, 2023 (SCI-Expanded) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 20 Sayı: 6
  • Basım Tarihi: 2023
  • Doi Numarası: 10.22111/ijfs.2023.44900.7922
  • Dergi Adı: Iranian Journal of Fuzzy Systems
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, zbMATH
  • Sayfa Sayıları: ss.105-122
  • Anahtar Kelimeler: (N,p,q) summability, convergence in Pringsheim’s sense, Double sequences of fuzzy numbers, fuzzy Korovkin theory, regularly varying sequences, slowly decreasing sequences, slowly oscillating sequences, weighted mean summability method
  • Uşak Üniversitesi Adresli: Evet

Özet

In this paper, our aim is to make a novel interpretation of relation between (N, p, q) method and P-convergence for double sequences of fuzzy numbers. In accordance with this aim, we derive some Tauberian conditions, controlling O-oscillatory behavior of a double sequence of fuzzy numbers in certain senses, from (N, p, q) summability to P-convergence with some restrictions on the weight sequences. As special cases, we indicate that O-condition of Hardy type with respect to (Pm) and (Qn) are Tauberian conditions for (N, p, q) summability under some additional conditions. In the sequel, we prove a fuzzy Korovkin-type approximation theorem by using the (N, p, q) summability method for fuzzy positive linear operators.