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

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

Pages : 1777-1787

Doi:10.15672/hujms.535246

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Publication Date : 2020-10-06

Article Type : Research Paper

Abstract :The aim of this paper is to find an upper bound of the fourth Hankel determinant $H_{4}insert ignore into journalissuearticles values(1);$ for a subclass of analytic functions associated with the right half of the Bernoulli`s lemniscate of the form $\leftinsert ignore into journalissuearticles values(x^{2}+y^{2}\right); ^{2}-2\leftinsert ignore into journalissuearticles values( x^{2}-y^{2}\right); =0$. 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