Criteria for strongly starlike and Φ-like functions

Abstract

In this article, we first obtain two theorems of first-order differential subordination. From these, we obtain some sufficient conditions for strongly starlike functions, close-to-convex functions with respect to k-symmetric points and Φ-like functions in the open unit disc. The results obtained generalize the related results of some authors, and some completely new results are also obtained.

Keywords:

• Strongly starlike functions
• Close-to-convex functions with respect to k-symmetric points
• Φ-like functions
• Subordination

AMS Subject Classifications::

• Primary 30C45
• Secondary 26D20

Acknowledgement

This research is partly supported by the National Natural Science Foundation of China (No. 10471048), the Doctoral Foundation of the Education Committee of China (No. 20050574002), the Natural Science Foundation of Fujian Province, China (No. Z0511013) and the Education Commission Foundation of Fujian Province, China (No. JB04038).