AIMS Mathematics (Mar 2020)
On analytic multivalent functions associated with lemniscate of Bernoulli
Abstract
In this paper, we establish some sufficient conditions for analyticfunctions associated with lemniscate of Bernoulli. In particular, wedetermine conditions on $\alpha $ such that\begin{equation*}1+\alpha \frac{z^{2+p\left( j-1\right) }g^{\prime }\left( z\right) }{pg^{j}\left( z\right) },\text{ for each }j=0,1,2,3,\end{equation*}are subordinated by Janowski function, then $\frac{g\left( z\right) }{z^{p}} \prec \sqrt{1+z},\ \left( z\in \mathfrak{D}\right) $. By choosing particular values of functions $g,$ we obtain some sufficient conditions for multivalent starlike functions associated with lemniscate of Bernoulli.
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