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

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].