Fixed coefficients for subclasses of starlike functions (Q919479)

Let \(f(z)=z-\sum^{\infty}_{m=2}a_ mz^ m\), \(m\geq 0\), satisfy the condition \[ \frac{D^{n+1}f(z)}{D^ nf(z)}=\frac{1+Aw(z)}{1+Bw(z)},\quad -1\leq A<B\leq 1 \] for w(z) analytic in the unit disc, \(w(0)=0\) and \(| w(z)| <1\). This class is denoted by \(S_ n(A,B).\) If further \(C_ 2=(B+1)(n+2)-(A+1)(n+1)\) and \(a_ 2=p(B-A)/c_ 2\), the function \(f(z)\in S_ n(A,B)\) is said to belong to \(S_ n(A,B,p)\). In the present paper the authors investigate the extreme points, sharp distortion theorems, coefficient bounds of \(S_ n(A,B,p)\).