On the Fekete-Szego problem for alpha-quasi-convex functions

Let Qα(α ≥0) denote the class of normalized analytic alpha-quasi-convex functions f, defined in the unit disc, D = {z : |z| < 1}, by the condition Re h (1 −α) f ′(z) g′(z) + α (zf ′(z))′ g′(z) i > 0, Where f(z) = z +P∞ n=2 anzn and where g(z) = z +P∞ n=2 bnzn is a convex univalent function in D. Sharp upper bounds are obtained for |a3 −µa2 2|, when µ ≥0.