In the paper we consider two coefficient functionals which are invariant in the class \(\mathcal {K}\) of convex functions. The invariance of a real-valued functional \(\Phi \) defined on the coefficients of functions in a given class \(A\subset \mathcal {A}\) means that the sharp bounds of \(\Phi (f)\) and \(\Phi (f^{-1})\) for \(f\in A\) are the same. We discuss the generalized second Hankel determinant \(|a_2a_4-\mu a_3^2|\) and a modification of the Zalcman functional \(|a_4-a_2a_3+a_2^3|\) . For the latter expression, the sharp estimation is derived not only for \(f\in \mathcal {K}\) but also for \(f\in \mathcal {K}_\beta \) , a class of strongly convex functions of order \(\beta \) .
