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International Journal of Mathematics and Mathematical Sciences
Volume 15, Issue 4, Pages 719-726
http://dx.doi.org/10.1155/S0161171292000930

Radius problems for a subclass of close-to-convex univalent functions

Mathematics Department, College of Science, King Saud University, Riyadh 11451, Saudi Arabia

Received 16 July 1990; Revised 26 December 1990

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

Let P[A,B], 1B<A1, be the class of functions p such that p(z) is subordinate to 1+Az1+Bz. A function f, analytic in the unit disk E is said to belong to the class Kβ*[A,B] if, and only if, there exists a function g with zg(z)g(z)P[A,B] such that Re(zf(z))g(z)>β, 0β<1 and zE. The functions in this class are close-to-convex and hence univalent. We study its relationship with some of the other subclasses of univalent functions. Some radius problems are also solved.