  We present new sets of proton fragmentation functions describing the
production of protons from the gluon and each of the quarks, obtained by a
global fit to all relevant data sets extracted from the single-inclusive
electron-positron annihilation. Our analysis is in good agreement with $e^+e^-$
annihilation data. We also impose the finite-mass effects of proton in our
calculations, a topic with a very little attention paid to in the literatures.
Proton mass effects turn out to be appreciable for the gluon and light quark
fragmentation functions, so the inclusion of finite-mass effects tends to
improve the overall description of the data by reducing the minimized $\chi^2$
values, significantly. As an application, we also apply the extracted
fragmentation functions to make our predictions for the scaled-energy
distribution of protons inclusively produced in top quark decays at
next-to-leading order, relying on the universality and scaling violations of
fragmentation functions.
