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International Journal of Mathematics and Mathematical Sciences
Volume 14 (1991), Issue 4, Pages 741-746
http://dx.doi.org/10.1155/S016117129100100X

On radii of convexity and starlikeness of some classes of analytic functions

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

Received 5 December 1989; Revised 21 March 1990

Copyright © 1991 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. Let P(α1) be the class of functions with positive real part greater than α1, 0α11. It is clear that p[A,B]P(1A1B)P[1,1]. The principal results in this paper are the determination of the radius of β-starlikeness and β-convexity of f(z) with β=1A1B, when f(z) is restricted to certain classes of univalent and analytic functions related vith P[A,B].