Tauberian Type Conditions Connecting Cesàro and Riesz Summability Methods of Different Orders

Author: Stepanyants S.A.

Source: Analysis Mathematica, Volume 27, Number 4, 2001 , pp. 287-318(32)

Publisher: Springer

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Abstract:

In the paper conditions are studied which ensure the equivalence of two given summability methods on the class of numerical series satisfying these conditions. One of these methods is the regular Cesàro method (C,w), which replaces the role of the convergence (C,0) the latter occurring in the classical Tauberian theorems. The other summability method considered is either the summability method (Rd, alpha ) by discrete Riesz means or the Cesàro method with (Rd, alpha ) with alpha > w. New Tauberian type conditions are obtained under which the corresponding Tauberian theorems are proved.