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