The data on mT spectra of K0S K+ and K- mesons produced in all inelastic p + p and p + pbar interactions in the energy range sqrt(s)NN=4.7-1800GeV are compiled and analyzed. The spectra are parameterized by a single exponential function, dN/(m_T*dm_T)=C exp(-m_T/T), and the inverse slope parameter T is the main object of study. The T parameter is found to be similar for K0S, K+ and K- mesons. It increases monotonically with collision energy from T~30MeV at sqrt(s)NN=4.7GeV to T~220MeV at sqrt(s)NN=1800GeV. The T parameter measured in p+p and p+pbar interactions is significantly lower than the corresponding parameter obtained for central Pb+Pb collisions at all studied energies. Also the shape of the energy dependence of T is different for central Pb+Pb collisions and p+p(pbar) interactions.