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We constrain the warm dark matter (WDM) particle mass with observations of cosmic reionization and CMB optical depth. We suggest that the gravitational waves (GWs) from stellar-mass black holes (BHs) could give a further constraint on WDM particle mass for future observations. The star formation rates (SFRs) of Population I/II (Pop I/II) and Population III (Pop III) stars are also derived. If the metallicity of the universe is enriched beyond the critical value of , the star formation shifts from Pop III to Pop I/II stars. Our results show that the SFRs are quite dependent on the WDM particle mass, especially at high redshifts. Combined with the reionization history and CMB optical depth derived from the recent Planck mission, we find that the current data require the WDM particle mass to be in a narrow range of . Furthermore, we suggest that the stochastic gravitational wave background (SGWB) produced by stellar BHs could give a further constraint on the WDM particle mass for future observations. For , with Salpeter (Chabrier) initial mass function (IMF), the SGWB from Pop I/II BHs has a peak amplitude of at , while the GW radiation at Hz is seriously suppressed. For , the SGWB peak amplitude is the same as that for , but a little lower at low frequencies. Therefore, it is hard to constrain the WDM particle mass by the SGWB from Pop I/II BHs. To assess the detectability of the GW signal, we also calculate the signal-to-noise ratios (S/N), which are and for and for the Einstein Telescope with Salpeter (Chabrier) IMF, respectively. The SGWB from Pop III BHs is very dependent on the WDM particle mass, the GW strength could be an order of magnitude different, and the frequency band could be two times different for and . Moreover, the SGWB from Pop III BHs with could be detected by the Laser Interferometer Space Antenna for one year of observation, but it cannot be detected for those with . [ABSTRACT FROM AUTHOR]