Fully Starlikeness and Fully Convexity for Bounded Harmonic Close-to-Convex Mappings

Abstract

In this article, analogous to the class of bounded analytic functions, defined by Zhongzhu and Owa (1992), we define a new subclass of bounded harmonic mappings. We determine the conditions for such mappings to be close-to-convex. We also determine sharp coefficient estimates, sufficient coefficient estimates, convolution and convex combination conditions. Moreover, we investigate radii of fully starlikeness and fully convexity for such mappings.