EMIS ELibM Electronic Journals PUBLICATIONS DE L'INSTITUT MATHÉMATIQUE (BEOGRAD) (N.S.)
Vol. 46(60), pp. 71--78 (1989)

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On the logarithmic derivative of some Bazilevic functions

S. Abdul Halim, R. R. London and D. K. Thomas

Department of Mathematics and Computer Science, University College of Swansea, Swansea SA2 8PP, Wales, Great Britain

Abstract: 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 $$ \operatorname{Re}e^{i\psi}(f'(z)(f(z)/z)^{\alpha-1}-\beta)>0 $$ 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

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Electronic fulltext finalized on: 2 Nov 2001. This page was last modified: 16 Nov 2001.

© 2001 Mathematical Institute of the Serbian Academy of Science and Arts
© 2001 ELibM for the EMIS Electronic Edition