An alternative proof of a Tauberian theorem for Abel summability method

• Çanak, Ibrahim ^[1] ; Totur, Ümit ^[2]
  1. [1] Ege University

     Ege University

     Turquía

     
  2. [2] Adnan Menderes University

     Adnan Menderes University

     Turquía

     
• Localización: Proyecciones: Journal of Mathematics, ISSN 0716-0917, ISSN-e 0717-6279, Vol. 35, Nº. 3, 2016, págs. 235-244
• Idioma: inglés
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• 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.