Radius problems for a subclass of close-to-convex univalent 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. 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, 0≤β<1 and z∈E. 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.