Note on Abel Summability of Double Series

Yeşilkayagil M., Başar F.

Numerical Functional Analysis and Optimization, vol.38, no.8, pp.1069-1076, 2017 (SCI-Expanded, Scopus)

  • Publication Type: Article / Article
  • Volume: 38 Issue: 8
  • Publication Date: 2017
  • Doi Number: 10.1080/01630563.2017.1316991
  • Journal Name: Numerical Functional Analysis and Optimization
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.1069-1076
  • Keywords: Abel convergence of double sequence, double sequence, double series, Pringsheim convergence
  • Uşak University Affiliated: Yes

Abstract

In this paper, we prove that if a double series converges to α, then the power series Σi, jai, jxiyj converges for all x,y∈(0,1) and its sum is α, as x,y∈(1−, 1−). But the converse of this is not true, in general. Our main goal is to show that the converse of the idea, above, is true under which condition/conditions.