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Explicit Formulas for the Coefficients of α-Convex Functions, α ≧ 0
Published online by Cambridge University Press: 20 November 2018
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Let the function
1
be analytic in the unit disk Δ = {z│ │z│ ≤ 1), with
there, and let α be a real number. Then f(z) is said to be α-convex in Δ if and only if the inequality
holds in Δ. The class of α-convex functions was introduced in [8] and was studied in detail in the series [5]–[10], where in particular it is shown that α-convex functions are univalent and starlike for all α (−∞≦ α ≦ + ∞), that is, the inequality
holds in Δ.
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- Copyright © Canadian Mathematical Society 1987
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