Bounded starlike functions of complex order (Q799828)

Suppose that \(M>{1\over2}\) and \(b\neq 0\), and denote by F(b,M) the class of analytic functions f(z) subject to the conditions \[ (i)\quad f(z)/z\neq 0,\quad (ii)\quad| b-1+zf'(z)(f(z))^{-1}-bM| <| bM| \] in the unit disk. Using standard techniques the authors obtain some coefficient bounds and the radius of starlikeness of the class F(b,M).