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International Journal of Mathematics and Mathematical Sciences
Volume 15, Issue 2, Pages 279-289
http://dx.doi.org/10.1155/S016117129200036X

On subclasses of close-to-convex functions of higher order

Mathematics Department, P.O. Box 2455, King Saud University, Riyadh 11451, Saudi Arabia

Received 30 October 1990; Revised 21 October 1991

Copyright © 1992 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.

Abstract

The classes Tk(ρ), 0ρ<1, k2, of analytic functions, using the class Vk(ρ) of functions of bounded boundary rotation, are defined and it is shown that the functions in these classes are close-to-convex of higher order. Covering theorem, arc-length result and some radii problems are solved. We also discuss some properties of the class Vk(ρ) including distortion and coefficient results.