RADII OF CONVEXITY AND STRONG STARLIKENESS FOR SOME CLASSES OF ANALYTIC-FUNCTIONS

Let phi(z) be an analytic function with positive real part on Delta = {z; \z\ < 1} with phi(0) = 1, phi'(0) > 0 which maps the unit disk Del ta onto a region starlike with respect to 1 and symmetric with respect to the real axis. Let ST(phi) denote the class of analytic functions f(z) with f(0) = 0 = f'(0) - 1 for which zf'(z)/f(z) < phi(z), z is an element of Delta. The radius of convexity of order beta of uniformly convex functions and the radius of starlikeness of order beta of the c lass ST(phi) are computed. The radii of strong starlikeness of certain classes of analytic functions are computed. (C) 1997 Academic Press.