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Proyecciones (Antofagasta)

Print version ISSN 0716-0917

Abstract

CANAK, Ibrahim  and  TOTUR, Umit. An alternative proof of a Tauberian theorem for Abel summability method. Proyecciones (Antofagasta) [online]. 2016, vol.35, n.3, pp.235-244. ISSN 0716-0917.  http://dx.doi.org/10.4067/S0716-09172016000300001.

Using a corollary to Karamata’s main theorem [Math. Z. 32 (1930), 319-320], we prove that ifa slowly decreasing sequence ofreal numbers is Abel summable, then it is convergent in the ordinary sense.

Keywords : Abel summability; slowly decreasing sequences; Tauberian conditions and theorems..

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