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Some Tauberian theorems for Euler and Borel summability

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  • J. A. Fridy
  • K. L. Roberts

Abstract

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

Suggested Citation

  • J. A. Fridy & K. L. Roberts, 1980. "Some Tauberian theorems for Euler and Borel summability," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 3, pages 1-8, January.
    • Handle: RePEc:hin:jijmms:276340
    DOI: 10.1155/S0161171280000531
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