Meromorphic Close-to-Convex Functions

A function g(z) = z +a₂z² + . . . , regular in |z| < 1 is said to be close-to-convex in |z| < 1 if there exists a function G(z) = z +b₂t² + . . . regular and starlike in |z| < 1 and such that

Re {z g'(z)/G(z)}>0 (|z|<1).            (1)