Tauberian Conditions Under which Convergence Follows from the Weighted Mean Summability and Its Statistical Extension for Sequences of Fuzzy Numbers
Küçük Resim Yok
Tarih
2022
Dergi Başlığı
Dergi ISSN
Cilt Başlığı
Yayıncı
Springer
Erişim Hakkı
info:eu-repo/semantics/closedAccess
Özet
Let (p(n)) be a sequence of nonnegative numbers such that p(0) > 0 and P-n:= Sigma(n)(k=0)p(k)->infinity as n -> infinity. Let (u(n)) be a sequence of fuzzy numbers. The weighted mean of (u(n)) is defined by t(n) := 1/P-n Sigma(n)(k=0)pkuk for n = 0,1,1,2,... It is known that the existence of the limit lim u(n) = mu(0) implies that lim t(n) = mu(0). For the existence of the limit st-lim t(n) = mu(0), we require the boundedness of (u(n)) in addition to the existence of the limit lim u(n) = mu(0). However, in general, the converse of this implication is not true. We establish Tauberian conditions, under which the existence of the limit lim u(n) = mu(0) follows from the existence of the limit lim t(n) = mu(0) or st-lim t(n) = mu(0). These Tauberian conditions are satisfied if (u(n)) satisfies the two-sided condition of Hardy type relative to (P-n).
Açıklama
Anahtar Kelimeler
Alpha
Kaynak
Ukrainian Mathematical Journal
WoS Q Değeri
Q4
Scopus Q Değeri
Q3
Cilt
73
Sayı
8
