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The Radius of Convexity of a Linear Combination of Functions in or uα
Published online by Cambridge University Press: 20 November 2018
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Labelle and Rahman [4] showed that if f , g ∈ , the normalized convex functions in the unit disc D, then has a radius of convexity at least as large as the smallest root of 1 – 3r + 2r2 — 2r3 = 0. Their method requires neither the properties of the arithmetic mean nor the strong geometric properties of ; indeed, the procedure works for a linear combination of functions from any linear invariant family of finite order.
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- Copyright © Canadian Mathematical Society 1973