Tauberian conditions under which convergence follows from cesàro summability of double integrals over r2+

2-s2.0-85077681145For 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 ?(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. © 2019, University of Nis. All rights reserved