TY - JOUR AU - Abdel-Gawad, H. R. PY - 2000/12/31 Y2 - 2024/03/29 TI - On the Fekete-Szego problem for alpha-quasi-convex functions JF - Tamkang Journal of Mathematics JA - Tamkang J. Math. VL - 31 IS - 4 SE - Papers DO - 10.5556/j.tkjm.31.2000.381 UR - https://journals.math.tku.edu.tw/index.php/TKJM/article/view/381 SP - 251-256 AB - <p>Let $ Q_\alpha(\alpha\ge 0)$ denote the class of normalized analytic alpha-quasi-convex functions $ f$, defined in the unit disc, $ D=\{z:|z|<1\}$, by the condition</p><p>$$ \hbox{Re}\left[(1-\alpha){f'(z)\over g'(z)}+ \alpha {(zf'(z))'\over g'(z)}\right]>0,$$</p><p>Where $ f(z)=z+\sum_{n=2}^\infty a_n z^n$ and where $ g(z)=z+\sum_{n=2}^\infty b_nz^n$ is a convex univalent function in $ D$. Sharp upper bounds are obtained for $ |a_3-\mu a_2^2|$, when $ \mu\ge 0$.</p> ER -