On strongly starlike multivalent functions of order β and type α

For analytic and p ‐valent functions f (z) in the open unit disk 𝕌, a new subclass S^*ₚ (α, β) consisting of the functions f (z) which are strongly starlike p ‐valent of order β and type α is introduced. The object of the present paper is to derive some sufficient conditions for f (z) to be in the class S^*ₚ (α, β). In particular, our results extend and improve some results given by Nunokawa et al. [J. Math. Anal. Appl. 212, 98–106 (1997)] (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)