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1 results

  • A General Tauberian Condition that Implies Euler Summability

  • Mangalam R. Parameswaran
  • Journal:
    Canadian Mathematical Bulletin / Volume 37 / Issue 3 / 01 September 1994
    Published online by Cambridge University Press:
    20 November 2018, pp. 393-398
    Print publication:
    01 September 1994
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  • Let V be any summability method (whether linear or conservative or not), 0 < p < 1 and s a real or complex sequence. Let Ep denote the matrix of the Euler method. A theorem is proved, giving a condition under which the V-summability of Eps will imply the Ep-summability of s. This extends, in generalized form, an earlier result of N. H. Bingham who considered the case where s is a real sequence and V = B (Borel's method). It is also proved that even for real sequences, the condition given in the theorem cannot be replaced by the condition used by Bingham.