On certain classes of close-to-convex functions
The author defines a class \(R_ n\) \((n=0,1,2,\dots)\) of analytic functions as follows: \(f(z)=z+\sum^ \infty_ 2 a_ k z^ k\) belongs to \(R_ n\) if and only if it is analytic and \(\text{Re}\bigl[z((D^ n f(z))'/(D^ n f(z)))\bigr]>0\) in the open unit disc. \(f\in K_ n\) if there exist \(g\in R_ n\) such that \(\text{Re}\bigl[z((D^ n f(z))'/(D^ n g(z)))\bigr]>0\). Several properties of the class \(K_ n\) like inclusion theorems, coefficient estimates, covering theorems are studied. The effect of certain integral operators generalizing the well- known Libera operators on \(K_ n\) are also studied.
scientific article; zbMATH DE number 179252