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On the Relation Between [f, g] and Aλ Summability
Published online by Cambridge University Press: 20 November 2018
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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.
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- Copyright © Canadian Mathematical Society 1974
References
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