Abel extensions of some classical Tauberian theorems


Gül E. , Albayrak M.

Creative Mathematics and Informatics, vol.28, pp.105-112, 2019 (Refereed Journals of Other Institutions)

  • Publication Type: Article / Article
  • Volume: 28
  • Publication Date: 2019
  • Title of Journal : Creative Mathematics and Informatics
  • Page Numbers: pp.105-112

Abstract

The well-known classical Tauberian theorems given for A (the discrete Abel mean) by Armitage

and Maddox in [Armitage, H. D and Maddox, J. I., Discrete Abel means, Analysis, 10 (1990), 177–186] is

generalized. Similarly the ”one-sided” Tauberian theorems of Landau and Schmidt for the Abel method are

extended by replacing lim As with Abel-lim Ain

(s): Slowly oscillating of fsng is a Tauberian condition of the

Hardy-Littlewood Tauberian theorem for Borel summability which is also given by replacing limt(Bs)t = `,

where t is a continuous parameter, with limn(Bs)n = `, and further replacing it by Abel-lim(Bik

(s))n = `,

where B is the Borel matrix method