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Tauberian- and Convexity Theorems for Certain (N,p,q)-Means

Published online by Cambridge University Press:  20 November 2018

Rüdiger Kiesel  and
Ulrich Stadtmüller
Rüdiger Kiesel
Affiliation:
Universität Ulm, Abteilung Stochastik D-89069 Ulm, Germany, e-mail: [email protected], [email protected]
Ulrich Stadtmüller
Affiliation:
Universität Ulm, Abteilung Stochastik D-89069 Ulm, Germany, e-mail: [email protected], [email protected]
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Abstract

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The summability fields of generalized Nörlund means (N,p*α,p), α ∈ Ν, are increasing with a and are contained in that of the corresponding power series method (P,p). Particular cases are the Cesàro- and Euler-means with corresponding power series methods of Abel and Borel. In this paper we generalize a convexity theorem, which is well-known for the Cesàro means and which was recently shown for the Euler means to a large class of generalized Nörlund means.

Keywords

40E05Power series methodsgeneralized Nörlund meansconvexity theoremsTauberian theorems
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 46 , Issue 5 , 01 October 1994 , pp. 982 - 994
Copyright
Copyright © Canadian Mathematical Society 1994

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