General Tauberian theorems for the Cesaro integrability of functions
Küçük Resim Yok
Tarih
2020
Yazarlar
Dergi Başlığı
Dergi ISSN
Cilt Başlığı
Yayıncı
Walter De Gruyter Gmbh
Erişim Hakkı
info:eu-repo/semantics/closedAccess
Özet
For a locally integrable function f on [0, infinity), we define F(t) = integral(t)(0) f(u) du and sigma(alpha)(t)= integral(t)(0) (1-u/t)(alpha) f(u) du for t > 0. The improper integral integral(infinity)(0) f(u) du is said to be (C, alpha) integrable to L for some alpha > -1 if the limit lim(x ->infinity) sigma(alpha)(t) = L exists. It is known that lim(x ->infinity) F(t) = l implies lim(x ->infinity) sigma(alpha)(t)= l for alpha > -1, but the converse of this implication is not true in general. in this paper, we introduce the concept of the general control modulo of non-integer order for functions and obtain some Tauberian conditions in terms of this concept for the (C, alpha) integrability method in order that the converse implication hold true. Our results extend the main theorems in [U. Totur and I. Canak, Tauberian conditions for the (C, alpha) integrability of functions, Positivity 21 (2017), no. 1, 73 83].
Açıklama
Anahtar Kelimeler
Cesaro integrability, (c, alpha) integrability, one-sided Tauberian condition, slow decreasing, Tauberian theorem and condition
Kaynak
Georgian Mathematical Journal
WoS Q Değeri
Q4
Scopus Q Değeri
Cilt
27
Sayı
4
