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On the Relation Between [f, g] and Aλ Summability

Published online by Cambridge University Press:  20 November 2018

Joaquin Bustoz
Joaquin Bustoz*
Affiliation:
University of Cincinnati, Cincinnati, Ohio
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First we will briefly define the [f, g] and Aλ summability methods. Let K = {w : |w| < 1}. T. H. Gronwall [3] introduced a general class of summability methods each of which involves a pair of functions f and g with the following properties. The function z = f (w) is analytic on \{1}, continuous and univalent on , with f (0) = 0, f (1) = 1, |f(w)| < 1 if w ∊ K. The inverse function w = f-1(z) is analytic on f (K)\{1}, and at z = 1

1.1

where γ ≧ 1, a > 0, and the quantity in brackets is a power series in 1 — z with positive radius of convergence.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 26 , Issue 4 , August 1974 , pp. 783 - 793
Copyright
Copyright © Canadian Mathematical Society 1974

References

1. Borwein, D., On a scale of Abel-type summability methods, Proc. Cambridge Philos. Soc. 52 (1957), 318–322.Google Scholar
2. Bustoz, J. and Wright, D., On Gronwall summability, Math. Z. 125 (1972), 177–183.Google Scholar
3. Gronwall, T. H., Summation of series and conformai mapping, Ann. of Math. 33 (1932), 101–117.Google Scholar
4. Kwee, B., On absolute de la Vallée Poussin summability, Pacific J. Math. 42 (1972), 689–693.Google Scholar
5. Szasz, O., On products of summability methods, Proc. Amer. Math. Soc. 3 (1952), 257–263.Google Scholar