Certain summability methods for functions and sequences are compared by their speeds of convergence. The authors are extending their results published in paper [9] for Riesz‐type families {Aα} (α > α0) of summability methods Aα. Note that a typical Riesz‐type family is the family formed by Riesz methods Aα= (R, α), α > 0. In [9] the comparative estimates for speeds of convergence for two methods Aγand Aβin a Riesz‐type family {Aα}were proved on the base of an inclusion theorem. In the present paper these estimates are improved by comparing speeds of three methods Aγ, Aβand Aδon the base of a Tauberian theorem. As a result, a Tauberian remainder theorem is proved. Numerical examples given in [9] are extended to the present paper as applications of the Tauberian remainder theorem proved here.
Šeletski, A., & Tali, A. (2010). Comparison of speeds of convergence in Riesz‐type families of summability methods. II. Mathematical Modelling and Analysis, 15(1), 103-112. https://doi.org/10.3846/1392-6292.2010.15.103-112
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