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International Journal of Mathematics and Mathematical Sciences
Volume 6, Issue 3, Pages 449-458

Subclasses of close-to-convex functions

Department of Mathematics, University of California, Davis, Davis 95616, California, USA

Received 24 January 1983

Copyright © 1983 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Let 𝒦[C,D], 1D<C1, denote the class of functions g(z), g(0)=g(0)1=0, analytic in the unit disk U={z:|z|<1} such that 1+(zg(z)/g(z)) is subordinate to (1+Cz)/(1+Dz), z ϵ U. We investigate the subclasses of close-to-convex functions f(z), f(0)=f(0)1=0, for which there exists g ϵ 𝒦[C,D] such that f/g is subordinate to (1+Az)/(1+Bz), 1B<A1. Distortion and rotation theorems and coefficient bounds are obtained. It is also shown that these classes are preserved under certain integral operators.