On fixed coefficients for a class of functions starlike with respect to symmetric points (Q2782468)

In their paper the authors consider the class \(TS_s^\ast (\alpha, \beta)\) of univalent analytic functions of the form NEWLINE\[NEWLINEf(z) = z - \sum ^\infty_{n=2} |a_n|z^nNEWLINE\]NEWLINE satisfying the conditions NEWLINE\[NEWLINE{\left|\frac{zf'(z)}{f(z)-f(-z)}-1\right|}< \beta {\left|\frac{ \alpha zf'(z)}{f(z)-f(-z)}+1\right|},\quad z \in D,\;0 \leq \alpha \leq 1,\;\tfrac{1}{2} < \beta \leq 1.NEWLINE\]NEWLINE For this class, they determine sharp coefficient estimates and prove the closure theorem and distortion theorem. Further they also establish the theorem that \(\forall f, g, h \in TS_s^\ast (\alpha, \beta)\), NEWLINE\[NEWLINE(1- \lambda) (f * g)+ \lambda (f *h) \in TS_s^{\ast} (\alpha, \beta).NEWLINE\]NEWLINENEWLINENEWLINEFor the entire collection see [Zbl 0980.00021].