Bulletin of the
Korean Mathematical Society BKMS

In the present investigation, sharp upper bounds of $|a_3-\mu a_2^2|$ for functions $f(z)=z+a_2z^2+a_3z^3+\cdots$ belonging to certain subclasses of starlike and convex functions with respect to symmetric points are obtained. Also certain applications of the main results for subclasses of functions defined by convolution with a normalized analytic function are given. In particular, Fekete-Szeg\"{o} inequalities for certain classes of functions defined through fractional derivatives are obtained.

Keywords: analytic functions, starlike functions, convex functions, subordination, coefficient problem, Fekete-Szego inequality

MSC numbers: 30C50, 30C45, 30C80