Close-to-Convex Multivalent Functions with Respect to Weakly Starlike Functions

Abstract

It is the object of this article to define close-to-convex multivalent functions in terms of weakly starlike multivalent functions. Six classes are defined, and shown to be equal. These generalize the class of close-to-convex functions developed by Livingston in the article, $p$-valent close-to-convex functions, Trans. Amer. Math. Soc. 115 (1965), 161-179.