On analytic multivalent functions associated with lemniscate of Bernoulli

• Main Authors: Qaiser Khan, Muhammad Arif, Bakhtiar Ahmad, Huo Tang
• Format: Article
• Language: English
• Published: AIMS Press 2020-03-01
• Series: AIMS Mathematics
• Subjects: multivalent functions; subordination; lemniscate of bernoulli; janowski functions
• Online Access: https://www.aimspress.com/article/10.3934/math.2020149/fulltext.html

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.