Abstract
Let $\mathcal{H}$ denote the class of analytic functions in the unit disc on the complex plane $\mathbf{C}$. Let $\mathcal{E}$ be a subclass of $\mathcal{H}$. If the operator $I:\mathcal{E}\rightarrow \mathcal{H}$ satisfies \begin{equation*} f(z)\prec g(z) \Rightarrow I[f](z)\prec I[g](z) \end{equation*} for all $f,g\in\mathcal{E}$, then it is called subordination-preserving operator on the class $\mathcal{E}$. In this work we consider the convexity of the Bernardi operator. We prove also that the Bernardi is the subordination-preserving operator on the class of starlike functions. The applications of main results are also presented.
Citation
Janusz Sokół. Mamoru Nunokawa. "On the subordination under Bernardi operator." Proc. Japan Acad. Ser. A Math. Sci. 89 (1) 11 - 14, January 2013. https://doi.org/10.3792/pjaa.89.11
Information