FEKETE-SZEGO PROBLEM FOR CERTAIN SUBCLASSES OF UNIVALENT FUNCTIONS

For 1 <= alpha < 2, let F(alpha) denote the class of locally univalent normalized analytic functions f(z) = z + Sigma(infinity)(n=2) a(n)z(n) in the unit disk D = {z is an element of C : vertical bar z vertical bar < 1} satisfying the condition Re(1+zf ''(z)/f'(z)) > alpha/2 - 1. In the present paper, we shall obtain the sharp upper bound for Fekete-Szego functional vertical bar a(3) - lambda a(2)(2)vertical bar for the complex parameter lambda.