A Study on Harmonic Functions

The class of functions that have bounded boundary rotation and bounded radius rotation are the generalization of the convex and the starlike functions, respectively. The concept of such functions was introduced by Löwner [1]. But he did not use the present terminology. It was Paatero [2, 3] who systematically developed their properties and made an exhaustive study of the class of functions that have bounded boundary rotation. We will examine in this paper, the subclass of $${\mathcal S}_{H}$$ that is related to the class of functions that have bounded radius rotation.