PUBLICATIONS DE L'INSTITUT MATHÉMATIQUE (BEOGRAD) (N.S.) Vol. 46(60), pp. 7178 (1989) 

On the logarithmic derivative of some Bazilevic functionsS. Abdul Halim, R. R. London and D. K. ThomasDepartment of Mathematics and Computer Science, University College of Swansea, Swansea SA2 8PP, Wales, Great BritainAbstract: For $\a>0$, $0\le\b<1$, let $B_0(\alpha,\beta)$ be the class of normalised analytic functions $f$ defined in the open unit disc $D$ such that $$ \operatorname{Re}e^{i\psi}(f'(z)(f(z)/z)^{\alpha1}\beta)>0 $$ for $z\in D$ and for some $\psi=\psi(f)\in R$. Upper and lower bounds for the logarithmic derivative $zf'/f$ for $f\in B_0(\alpha,\beta)$ are obtained. Classification (MSC2000): 30C45 Full text of the article:
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