On a class of close-to-convex functions

Silverman, H.

doi:10.1090/S0002-9939-1972-0313494-X

On a class of close-to-convex functions
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Proc. Amer. Math. Soc. 36 (1972), 477-484 Request permission

Abstract:

We look at functions $f(z)$ for which there correspond functions $\phi (z)$ convex of order $\alpha$ such that $\operatorname {Re} \{ f’(z)/\phi ’(z)\} \geqq \beta$. We examine the influence of the second coefficient of $\phi (z)$ on this class. In particular, distortion, covering, and radius of convexity theorems are proved.

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