Extended Tauberian Theorem for the weighted mean Method of Summability

• Date: 2013
• Main Authors: Çanak, І., Totur, Ü., Чанак, І., Тотур, Ю.
• Format: Article
• Language: English
• Published: Institute of Mathematics, NAS of Ukraine 2013
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/2478
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

We prove a new Tauberian-like theorem. For a real sequence u = (u n ), on the basis of the weighted mean summability of its generator sequence (V (0) n,p (∆u)) and some other conditions, this theorem establishes the property of slow oscillation of the indicated sequence.