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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 (x 2 + y 2) 2 −2 (x 2 − y 2) = 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.

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