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Context. Molecular clouds near the H II regions tend to harbor more luminous protostars. Aims. Our aim in this paper is to investigate whether or not radiation-driven implosion mechanism enhances luminosity of protostars near regions of high-ionizing fluxes. Methods. We performed numerical simulations to model collapse of cores exposed to UV radiation from O stars. We investigated dependence of mass loss rates on the initial density profiles of cores and variation of UV fluxes. We derived simple analytic estimates of accretion rates and final masses of protostars. Results. Radiation-driven implosion mechanism can increase accretion rates of protostars by 1-2 orders of magnitude. On the other hand, mass loss due to photo-evaporation is not large enough to have a significant impact on the luminosity. The increase of accretion rate makes luminosity 1-2 orders higher than those of protostars that form without external triggering. Conclusions. Radiation-driven implosion can help explain the observed higher luminosity of protostars in molecular clouds near H II regions., Comment: 9 pages, 6 figures, accepted for publication in Astronomy and Astrophysics