Fekete-Szegő inequalities for starlike functions with respect to \(k\)-symmetric points of complex order (Q2338814)

Summary: Sharp upper bounds of \(| a_3 - \mu a_2^2 |\) for the function \(f(z)=z+\sum^{\infty}_{m=2} a_mz^m\) belonging to certain subclass of starlike functions with respect to \(k\)-symmetric points of complex order are obtained. Also, applications of our results to certain functions defined through convolution with a normalized analytic function are given. In particular, Fekete-Szegő inequalities for certain classes of functions defined through fractional derivatives are obtained.