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Comparison of speeds of convergence in Riesz-type families of summability methods; pp. 70–80

Full article in PDF format | doi: 10.3176/proc.2008.2.02

Anna Šeletski, Anne Tali

We deal with Riesz-type families (see Proc. Estonian Acad. Sci. Phys. Math., 2002, 51, 18–34 and Acta Sci. Math. (Szeged), 2004, 70, 639–657) of summability methods Aα for converging functions and sequences. The methods Aα in a Riesz-type family depend on a continuous parameter α, and are connected through certain generalized integral Nörlund methods. By extending and applying the results of Stadtmüller and Tali (Anal. Math., 2003, 29, 227–242), we compare speeds of convergence in a Riesz-type family. As expected, the speed of convergence cannot increase if we switch from one summability method to a stronger one. Comparative estimations for speeds are found. In particular, the families of integral Riesz methods, generalized integral Nörlund methods, and Abel- and Borel-type summability methods are considered. Numerical examples are given.

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