An alternative proof of a Tauberian theorem for Abel summability method

Ibrahim Çanak, Ümit Totur

Resumen


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

Palabras clave


Abel summability; slowly decreasing sequences; Tauberian conditions and theorems; sumabilidad abeliana; secuencias lentamente decrecientes; condiciones y teoremas de Tauber.

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Referencias


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DOI: http://dx.doi.org/10.4067/S0716-09172016000300001

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