  Low-temperature magnetization curves of the classical frustrated
ferromagnetic chain in the external magnetic field near the transition point
between the ferromagnetic and the helical phases is studied. It is shown that
the calculation of the partition function in the scaling limit reduces to the
solution of the Schr\"{o}dinger equation of the special form for the quantum
particle. It is proposed that the magnetization of the classical model in the
ferromagnetic part of the phase diagram including the transition point defines
the universal scaling function which is valid for quantum model as well.
Explicit analytical formulae for the magnetization are given in the limiting
cases of low and high magnetic fields. The influence of the easy-axis
anisotropy on the magnetic properties of the model is studied. It is shown that
even small anisotropy essentially changes the behavior of the susceptibility in
the vicinity of the transition point.
