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 H₄(1) for a subclass of analytic functions associated with the right half of the Bernoulli's lemniscate of the form (x²+y²) ²-2( x²-y²) =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 P of functions with positive real part.***************************************************************************************************************************