Subclasses of Multivalent Starlike and Convex Functions

Abstract

Subclasses of $p$-valent starlike and convex functions in the unit disk in the complex plane are investigated. Every $p$-valent convex function in a subclass is shown to belong to its corresponding subclass of starlike functions. A necessary and sufficient condition for functions to belong to these classes is obtained. Subordination properties, and sharp distortion, growth, covering and rotation estimates are obtained for these classes. Convolution results with prestarlike functions are also derived.