The Fekete-Szego Theorem for a Certain Class of Analytic Functions

In this paper, we discuss a well known class studied by many authors including Ramesha et al. and Janteng, few to mention. Next, we extend the class to a wider class of functions f denoted by u(alpha)(beta), which are normalized and univalent, in the open unit disk D={z:vertical bar z vertical bar<1} satisfying the condition: Re[a z(2)f(n)(z)/g(z) + zf'(z)/g(z)) > 0, 0 <= alpha < 1, where g is an element of S* (beta), g(z)not equal 0 is a normalized starlike function of order beta, for 0 = beta < 1. For f is an element of u(alpha)(beta) we shall obtain sharp upper bounds for the Fekete-Szego functional vertical bar a(3) - mu a(2)(2 vertical bar) when mu is real.