Note on Abel Summability of Double Series. (3rd August 2017)

• Record Type: Journal Article
• Authors: Yeşilkayagil, Medine; Başar, Feyzi
• Is Part Of: Numerical functional analysis and optimization. Volume 38:Number 8(2017)
• Page Start: 1069
• Page End: 1076
• Publication Date: 2017-08-03
• Subjects: Abel convergence of double sequence -- double sequence -- double series -- Pringsheim convergence; 40C05 -- 40G10; Functional analysis -- Periodicals; Numerical analysis -- Periodicals; Mathematical optimization -- Periodicals; Numerical Analysis, Computer-Assisted; 515.705
• DOI: 10.1080/01630563.2017.1316991
• Languages: English
• ISSNs: 0163-0563

Abstract

ABSTRACT: In this paper, we prove that if a double series converges to α, then the power series converges for all x, y ∈(0, 1) and its sum is α, as . 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.