  We investigate a competition of tendencies towards ferromagnetic and
incommensurate order in two-dimensional fermionic systems within functional
renormalization group technique using temperature as a scale parameter. We
assume that the Fermi surface (FS) is substantially curved, lies in the
vicinity of van Hove singularity points and perform an account of the
self-energy corrections. It is shown that the character of magnetic
fluctuations is strongly asymmetric with respect to the Fermi level position
relatively to van Hove singularity (VHS). For the Fermi level above VHS we find
at low temperatures dominant incommensurate magnetic fluctuations, while below
VHS level we find indications for ferromagnetic ground state. In agreement with
the Mermin-Wagner theorem, at finite temperatures and in small magnetic fields
we obtain rather small magnetization, which appears to be a power-law function
of magnetic field. It is found that the FS curvature is slightly increased by
correlation effects, and the renormalized bandwidth decreases at sufficiently
low temperatures.
