RADIUS PROBLEMS IN A CERTAIN SUBCLASS OF CLOSE-TO-CONVEX FUNCTIONS

Let K-s(gamma) denote the class of all analytic functions f in the unit disc u with the normalization f(0) = f'(0) - 1 = 0 and satisfying the condition R-e[x(2) f' (x)/(g(x)g(-x))] > gamma, x is an element of u for some g starlike of order 1/2. In this paper some basic geometric properties for the class K-s(gamma) are investigated. Among others things, the radius of convexity of f is an element of k(s) (gamma) and the sharp upper and lower bounds for vertical bar arg f'(z)vertical bar are determined.