On analytic functions related with generalized Robertson functions

摘要

Analytic functions f are called Robertson functions for which is -spiral-like. This concept is generalized by several authors and a class real, of analytic functions is introduced and studied. It is noted that the functions in are of bounded boundary rotation and consists of Robertson functions.In this paper, we use the class to define a new class of analytic functions which unifies a number of classes previously studied such as the class of close-to-convex functions of higher order. Some interesting properties of this class, including coefficient problems, inclusion results and a sufficient condition for univalency are studied.