Tauberian Conditions Under Which Convergence Follows from Cesaro Summability of Double Integrals Over R-+(2)


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Findik G., ÇANAK İ.

FILOMAT, vol.33, no.11, pp.3425-3440, 2019 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 33 Issue: 11
  • Publication Date: 2019
  • Doi Number: 10.2298/fil1911425f
  • Title of Journal : FILOMAT
  • Page Numbers: pp.3425-3440

Abstract

For a real- or complex-valued continuous function f over R-+(2) := [0, infinity) x [0, infinity), we denote its integral over [0, u] x [0, v] by s(u, v) and its (C, 1, 1) mean, the average of s(u, v) over [0, u] x [0, v], by sigma(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 R-+(2). 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 Ces`aro summability methods of double integrals over [0, u] x [0, v] under which convergence of s(u, v) follows from integrability of s(u, v) in different senses.