Tauberian conditions under which convergence follows from cesàro summability of double integrals over r<sup>2</sup>+
Makaleler > Tam Makale · 2019
Yazarlar: Gökşen Fındık, İbrahim ÇANAK
Filomat, SCI Expanded İndekslerine Giren Dergi, Uluslararası, Scopus, 2019, cilt 33, ss 3425-3440
DOI: 10.2298/FIL1911425F
Özet
For a real-or complex-valued continuous function f over R2+:= [0, ∞) × [0, ∞), we denote its integral over [0, u] × [0, v] by s(u, v) and its (C, 1, 1) mean, the average of s(u, v) over [0, u] × [0, v], by σ(u, v). The other means (C, 1, 0) and (C, 0, 1) are defined analogously. We introduce the concepts of backward differences and the Kronecker identities in different senses for double integrals over R2+. We give one-sided and two-sided Tauberian conditions based on the difference between double integral of s(u, v) and its means in different senses for Cesàro summability methods of double integrals over [0, u] × [0, v] under which convergence of s(u, v) follows from integrability of s(u, v) in different senses.