Uniformly starlike and convex functions and other related classes of univalent functions (Q2769213)

The authors investigate the classes of functions called uniformly convex and uniformly starlike, and some related classes of univalent functions. They also introduce a class of functions \(ST(\zeta)\) which is given by the property that the image of any circular arc centered at \(\zeta\) and contained in the unit disk \(U\) is starlike with respect to \(f(\zeta)\). These functions are normalized so that \(f(\zeta)= f'(\zeta)- 1=0\). Corresponding to \(ST(\zeta)\) they define \(CV(\zeta)\) such that \(f\in CV(\zeta)\) if and only if \((z-\zeta) f'(z)\in ST(\zeta)\).NEWLINENEWLINENEWLINEThese results have been substantially improved and generalized by these authors in later papers.