M. ARİF, Sadaf UMAR, Mohsan RAZA, Teodor BULBOACA, Muhammad Umar FAROOQ, Hasan KHAN

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

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,

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Hacettepe Journal of Mathematics and Statistics-Cover

Yayın Aralığı: Yılda 6 Sayı
Başlangıç: 2002
Yayıncı: Hacettepe Üniversitesi Fen Fakultesi

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