Tauberian theorems for the Cesàro summability method of regularly generated double integrals
Articles > Article · 2023
Authors: Gökşen Fındık, İbrahim ÇANAK
FILOMAT, Journal Indexed in SCI Expanded, International, WoS, 2023, vol 37, pp 2969-2980
DOI: 10.2298/FIL2309969F
Summary
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)).