Log-Harmonic Mappings Associated With the Sine Function

Abstract

In this paper, we define new subclasses STlh (s) and CSTlh (s) of sine starlike log-harmonic mappings and sine close-to-starlike log-harmonic mappings, respectively, defined in the open unit disc D. We investigate representation theorem and integral representation theorem for functions in the class STlh (s). Further, we determine radius of starlikeness for functions in the classes STlh (s) and CSTlh (s).