On fourth Hankel determinant for functions associated with Bernoulli's lemniscate

Year 2020, Volume: 49 Issue: 5, 1777 - 1787, 06.10.2020

M. Arif , Sadaf Umar Mohsan Raza , Teodor Bulboaca , Muhammad Umar Farooq Hasan Khan

https://doi.org/10.15672/hujms.535246

Cited By: 10

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.

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Keywords

differential subordination , Bernoulli's lemniscate , Hankel determinants , starlike functions

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