Fekete-Szegö Problems for Quasi-Subordination Classes

Abstract

An analytic function $f$ is quasi-subordinate to an analytic function $g$, in the open unit disk if there exist analytic functions $\phi$ and $w$, with $|\phi (z)|\le 1$, $w(0)=0$ and such that $f(z)=\phi (z)g(w(z))$. Certain subclasses of analytic univalent functions associated with quasi-subordination are defined and the bounds for the Fekete-Szegö coefficient functional $|a_3-\mu a_2^2|$ for functions belonging to these subclasses are derived.