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Explicit Formulas for the Coefficients of α-Convex Functions, α ≧ 0

Published online by Cambridge University Press:  20 November 2018

Pavel G. Todorov
Pavel G. Todorov*
Affiliation:
20 Lenin Avenue, Plovdiv, Bulgaria
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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.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 39 , Issue 4 , 01 August 1987 , pp. 769 - 783
Copyright
Copyright © Canadian Mathematical Society 1987

References

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