A differential operator and its applications to certain multivalently analytic functions. (English) Zbl 1138.30005
Using the well-known Jack’s Lemma, certain properties of functions defined by \(q\)th derivative of \(p\)-valent functions were obtained. As consequences, sufficient conditions for \(p\)-valent starlikeness, convexity and close-to-convexity are obtained.
Reviewer: V. Ravichandran (Delhi)
MSC:
| 30C45 | Special classes of univalent and multivalent functions of one complex variable (starlike, convex, bounded rotation, etc.) |
