  The production of D mesons in proton-proton collisions at the LHCb detector
is studied. We consider the single production of D^0, D^+, D^star, and D_s^+
mesons and correlation spectra in the production of DbarD and DD pairs at the
sqrt{S}=7 TeV and sqrt{S}=13 TeV. In case of the single D-meson production we
calculate differential cross sections over transverse momentum p_T while in the
pair DbarD,DD-meson production the cross sections are calculated over the
azimuthal angle difference, rapidity difference, invariant mass of the pair M
and over the p_T of the one meson from a pair. The cross sections are obtained
at the leading order of the parton Reggeization approach using
Kimber-Martin-Ryskin unintegrated parton distribution functions in a proton. To
describe the D-meson production we use universal scale-dependent c-quark and
gluon fragmentation functions fitted to e^+e^- annihilation data from CERN
LEP1. Our predictions find a good agreement with the LHCb Collaboration data
within uncertainties and without free parameters.
