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.
Similar content being viewed by others
References
Ï. Çanak and Ü. Totur, “Some Tauberian theorems for the weighted mean methods of summability,” Comput. Math. Appl., 62, 2609–2615 (2011).
Ï. Çanak and Ü. Totur, “Some Tauberian theorems for Borel summability methods,” Appl. Math. Lett., 23, No. 3, 302–305 (2010).
Ï. Çanak and Ü. Totur, “A condition under which slow oscillation of a sequence follows from Cesàro summability of its generator sequence,” Appl. Math. Comput., 216, No. 5, 1618–1623 (2010).
Ï. Çanak, Ü. Totur, and B. P. Allahverdiev, “Tauberian conditions with controlled oscillatory behavior,” Appl. Math. Lett., 25, No. 3, 252–256 (2012).
Ï. Çanak, Ü. Totur, and M. Dik, “One-sided Tauberian conditions for (A, k) summability method,” Math. Comput. Modelling, 51, No. 5-6, 425–430 (2010).
Č. V. Stanojević, “Analysis of divergence: control and management of divergent process,” Graduate Research Seminar Lecture Notes, Ed. ˙Ï. Çanak, Univ. Missouri-Rolla, Fall (1998), 56 p.
G. H. Hardy, Divergent Series, Clarendon Press, Oxford (1949).
H. Tietz, “Schmidtsche Umkehrbedingungen für Potenzreihenverfahren,” Acta Sci. Math., 54, No. 3-4, 355–365 (1990).
H. Tietz and K. Zeller, “Tauber-Bedingungen für Verfahren mit Abschnittskonvergenz,” Acta Math. Hung, 81, No. 3, 241–247 (1998).
F. Móricz and B. E. Rhoades, “Necessary and sufficient Tauberian conditions for certain weighted mean methods of summability,” Acta Math. Hung., 66, No. 1-2, 105–111 (1995).
Ï. Çanak, “An extended Tauberian theorem for the (C, 1) summability method,” Appl. Math. Lett., 21, No. 1, 74–80 (2008).
Author information
Authors and Affiliations
Additional information
Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 65, No. 7, pp. 928–935, July, 2013.
Rights and permissions
About this article
Cite this article
Çanak, Ï., Totur, Ü. Extended Tauberian Theorem for the weighted mean Method of Summability. Ukr Math J 65, 1032–1041 (2013). https://doi.org/10.1007/s11253-013-0839-x
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11253-013-0839-x