Bounded starlike functions of complex order. (English) Zbl 0548.30004

Nasr, M. A.; Aouf, M. K.

Proc. Indian Acad. Sci., Math. Sci. 92, 97-102 (1983).

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).

Reviewer: E.Złotkiewicz

MSC:

30C45

Special classes of univalent and multivalent functions of one complex variable (starlike, convex, bounded rotation, etc.)

Keywords:

bounded spirallike functions; coefficient bounds; radius of starlikeness

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