On the Fekete-Szego problem for alpha-quasi-convex functions - Abdel-Gawad, H. R. (Tamkang Journal of Mathematics, 2000)
Let Q_α(α0) denote the class of normalized analytic alpha-quasi-convex functions f, defined in the unit disc, D={z:|z|<1}, by the condition Re[(1-α)f'(z)g'(z)+ α (zf'(z))'g'(z)]>0, Where f(z)=z+_n=2^∞ a_n z^n and where g(z)=z+_n=2^∞ b_nz^n is a convex univalent function in D. Sharp upper bounds are obtained for |a_3-μ a_2^2|, when μ0.