International Journal of Mathematics and Mathematical Sciences
Volume 14 (1991), Issue 4, Pages 741-746
doi: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 Khalida Inayat Noor. 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], −1≤B<A≤1, 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, 0≤α1≤1. It is clear that
p[A,B]⊂P(1−A1−B)⊂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=1−A1−B, when f(z) is restricted to certain classes of univalent
and analytic functions related vith P[A,B].