Log-Harmonic mappings associated with the sine function

Abstract

In this paper, we define new subclasses $\mathcal{ST}_{lh}(s)$ and $\mathcal{CST}_{lh}(s)$ of sine starlike log-harmonic mappings and sine close-to-starlike log-harmonic mappings, respectively, defined in the open unit disc ${\mathbb D}$. We investigate representation theorem and integral representation theorem for functions in the class $\mathcal{ST}_{lh}(s)$. Further, we determine radius of starlikeness for functions in the classes $\mathcal{ST}_{lh}(s)$ and $\mathcal{CST}_{lh}(s)$.

Keywords

• starlike function
• sine starlike log-harmonic mapping
• radius of starlikeness
• sine close-to-starlike log-harmonic mapping

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