Tauberian theorems for the Cesàro summability method of regularly generated double integrals
Makaleler > Tam Makale · 2023
Yazarlar: Gökşen Fındık, İbrahim ÇANAK
FILOMAT, SCI Expanded İndekslerine Giren Dergi, Uluslararası, Wos, 2023, cilt 37, ss 2969-2980
DOI: 10.2298/FIL2309969F
Özet
For a continuous function over R+2:= [1, ∞) × [1, ∞), we denote its integral over [1, x] × [1, y] by h(x, y) =∫ x ∫y (u, v)dudv and its (C, 1, 1) mean, the average of h(x, y) over [1, x] × [1, y], by t(h(x, y)) = 1 1 (xy)∫−1 x ∫y h(u, v)dudv. Analogously, the other means (C, 1, 0) and (C, 0, 1) can be defined. In this paper, 1 1 we introduce the concept of regularly generated double integrals in senses (1, 1), (1, 0) and (0, 1) and obtain Tauberian conditions in terms of the regularly generated double integrals in senses (1, 1), (1, 0) and (0, 1) under which convergence of h(x, y) follows from that of t(h(x, y)).