Open Access
January 2013 On the subordination under Bernardi operator
Janusz Sokół, Mamoru Nunokawa
Proc. Japan Acad. Ser. A Math. Sci. 89(1): 11-14 (January 2013). DOI: 10.3792/pjaa.89.11


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.


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Janusz Sokół. Mamoru Nunokawa. "On the subordination under Bernardi operator." Proc. Japan Acad. Ser. A Math. Sci. 89 (1) 11 - 14, January 2013.


Published: January 2013
First available in Project Euclid: 7 January 2013

zbMATH: 1269.30022
MathSciNet: MR3017721
Digital Object Identifier: 10.3792/pjaa.89.11

Primary: 30C45
Secondary: 30C80

Keywords: Bernardi operator , Convex functions , Hadamard product , Libera operator , preserving operator , Subordination

Rights: Copyright © 2013 The Japan Academy

Vol.89 • No. 1 • January 2013
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