The sharp estimates for certain coefficient inequalities for transforms of a starlike function associated with Bernoulli’s lemniscate

Abstract

This paper contains an estimation of sharp upper bound (UB) for the Hankel determinant of specific orders concerning the [Formula: see text][Formula: see text]-root transform [Formula: see text] for a subfamily of holomorphic functions associated with the right half of Bernoulli’s lemniscate. The practical tools applied in the derivation of our main results are the coefficient inequalities of the Carathéodory class [Formula: see text]