  In this paper, by means of the classical Lagrange inversion formula, we
establish a general nonlinear inverse relations which is a partial solution to
the problem proposed in the paper [J. Wang, Nonlinear inverse relations for the
Bell polynomials via the Lagrange inversion formula, J. Integer Seq., Vol. 22
(2019), Article 19.3.8.
(https://cs.uwaterloo.ca/journals/JIS/VOL22/Wang/wang53.pdf). As applications
of this inverse relation, we not only find a short proof of another nonlinear
inverse relation due to Birmajer et al., but also set up a few convolution
identities concerning the Mina polynomials.
