AIMS Mathematics (2020-03-01)

On analytic multivalent functions associated with lemniscate of Bernoulli

  • Qaiser Khan,
  • Muhammad Arif,
  • Bakhtiar Ahmad,
  • Huo Tang

DOI
https://doi.org/10.3934/math.2020149
Journal volume & issue
Vol. 5, no. 3
pp. 2261 – 2271

Abstract

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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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