- Hacettepe Journal of Mathematics and Statistics
- Vol: 49 Issue: 5
- On fourth Hankel determinant for functions associated with Bernoulli's lemniscate
On fourth Hankel determinant for functions associated with Bernoulli's lemniscate
Authors : M. Arif, Sadaf Umar, Mohsan Raza, Teodor Bulboaca, Muhammad Umar Farooq, Hasan Khan
Pages : 1777-1787
Doi:10.15672/hujms.535246
View : 8 | Download : 2
Publication Date : 2020-10-06
Article Type : Research
Abstract :The aim of this paper is to find an upper bound of the fourth Hankel determinant $H_{4}(1)$ for a subclass of analytic functions associated with the right half of the Bernoulli's lemniscate of the form $\left(x^{2}+y^{2}\right) ^{2}-2\left( x^{2}-y^{2}\right) =0$. The problem is also discussed for 2-fold and 3-fold symmetric functions. The key tools in the proof of our main results are the coefficient inequalities for class $\mathcal{P}$ of functions with positive real part. ***************************************************************************************************************************Keywords : differential subordination, Bernoulli's lemniscate, Hankel determinants, starlike functions