A note on certain subclasses of spiral-like functions (Q1093033)

The object of the present paper is first to prove a representation formula and a distortion theorem for functions belonging to the classes \(\phi _ p(\alpha,a,b)\) of \(\alpha\)-spirallike functions introduced here, and then to determining the radius of starlikeness for this class. By specializing the various parameters involved, the corresponding results for the function classes studied earlier (for example, by \textit{Z. J. Jakubowski} [Bull. Acad. Polon. Sci., Sér. Sci. Math. Astron. Phys. 19, 811-815 (1971; Zbl 0224.30029); see also Ann. Polon. Math. 26, 305- 313 (1972; Zbl 0241.30022)], \textit{S. Owa} [Pure Appl. Math. Sci. 15, 29- 36 (1982; Zbl 0516.30009)], \textit{H. Silverman} [Rev. Roum. Math. Pures Appl. 23, 1093-1099 (1978; Zbl 0389.30005)], and \textit{E. M. Silvia} [Tamkang J. Math. 14, 161-169 (1983; Zbl 0538.30006)]) can be derived.