International Journal of Mathematics and Mathematical Sciences

International Journal of Mathematics and Mathematical Sciences / 1980 / Article

Open Access

Volume 3 |Article ID 276340 | https://doi.org/10.1155/S0161171280000531

J. A. Fridy, K. L. Roberts, "Some Tauberian theorems for Euler and Borel summability", International Journal of Mathematics and Mathematical Sciences, vol. 3, Article ID 276340, 8 pages, 1980. https://doi.org/10.1155/S0161171280000531

Some Tauberian theorems for Euler and Borel summability

Received06 Aug 1979
Revised07 Dec 1979

Abstract

The well-known summability methods of Euler and Borel are studied as mappings from 1 into 1. In this setting, the following Tauberian results are proved: if x is a sequence that is mapped into 1 by the Euler-Knopp method Er with r>0 (or the Borel matrix method) and x satisfies n=0|xnxn+1|n<, then x itself is in 1.

Copyright © 1980 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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