Coefficient inequalities for a subclass of starlike functions
The authors investigate subclasses of the well known class S of univalent functions. \(T^*(a,b)\subset S\) is the subclass of functions \(f\in S\) satisfying for \(| z| <1:\) \[ | (zf'(z)/f(z))-a| \leq b,\quad a\quad real\quad and\quad b\geq 0 \] s.t. \(f(z)=z- \sum^{\infty}_{n=2}a_ nz^ n\), \(a_ n\geq 0\). The author finds various properties of these classes like coefficients' estimates, extreme points and connections with the class of \(\alpha\)-starlike functions. The class \(T^*_ 2(a,b)\subset T^*(a,b)\) is the class of functions in \(T^*(a,b)\) where \(a<1\) and \(a_{2k+1}=0\) for \(k\geq 1\). Further results are proved also for this class. Most of the results are sharp.
scientific article; zbMATH DE number 3935384