The Schechter-Valle theorem states that a positive observation of neutrinoless double-beta ($0 u beta beta$) decays implies a finite Majorana mass term for neutrinos when any unlikely fine-tuning or cancellation is absent. In this note, we reexamine the quantitative impact of the Schechter-Valle theorem, and find that current experimental lower limits on the half-lives of $0 u beta beta$-decaying nuclei have placed a restrictive upper bound on the Majorana neutrino mass $|delta m^{ee}_ u| < 7.43 times 10^{-29}~{rm eV}$ radiatively generated at the four-loop level. Furthermore, we generalize this quantitative analysis of $0 u beta beta$ decays to that of the lepton-number-violating (LNV) meson decays $M^- to {M^prime}^+ + ell^-_alpha + ell^-_beta$ (for $alpha$, $beta$ = $e$ or $mu$). Given the present upper limits on these rare LNV decays, we have derived the loop-induced Majorana neutrino masses $|delta m^{ee}_ u| < 9.7 times 10^{-18}~{rm eV}$, $|delta m^{emu}_ u| < 1.6 times 10^{-15}~{rm eV}$ and $|delta m^{mu mu}_ u| < 1.0 times 10^{-12}~{rm eV}$ from $K^- to pi^+ + e^- + e^-$, $K^- to pi^+ + e^- + mu^-$ and $K^- to pi^+ + mu^- + mu^-$, respectively. A partial list of radiative neutrino masses from the LNV decays of $D$, $D_s^{}$ and $B$ mesons is also given.
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