Relations of stellar mass between electron temperature-based metallicity of star-forming galaxies in a wide mass range

We select 947 star-forming galaxies from SDSS-DR7 with [O~{\sc iii}]$\lambda$4363 emission lines detected at a signal-to-noise {ratio }larger than 5$\sigma$. Their electron temperatures and direct oxygen abundances are {then }determined. {W}e compare the results from different methods. $t_2${, the} electron temperature in {the }low ionization region{,} estimated from $t_3${, that} in {the }high ionization region{,} {is} compared {using} three analysis relations between $t_2-t_3${. These} show obvious differences, which result in some different ionic oxygen abundances. The results of $t_3$, $t_2$, {${\mathrm{O}}^{++}$/${\mathrm{H}}^{+}$} and {${\mathrm{O}}^{+}$/${\mathrm{H}}^{+}$} derived by using methods from IRAF and literature are also compared. The ionic abundances ${\mathrm{O}}^{++}$/${\mathrm{H}}^{+}$ {are} higher than ${\mathrm{O}}^{+}$/${\mathrm{H}}^{+}$ for most cases. The{ different} oxygen abundances derived from $T_{\mathrm{e}}$ and the strong-line ratios show {a }clear discrepancy, which is more obvious following increasing stellar mass and strong-line ratio $R_{23}$. The sample{ of} galaxies from SDSS {with} detected [O~{\sc iii}]$\lambda$4363 have lower metallicites and higher {star formation rates}, {so} they may not be typical representatives of the whole{ population of} galaxies. Adopting data objects from {Andrews & Martini}, {Liang et al.} and {Lee et al.} data, we derive new relations of stellar mass and metallicity for star-forming galaxies in a much wider stellar mass range: from ${10}^6{M}_{\odot }$ to ${10}^{11}{M}_{\odot }$.