  In this article we have analytically deduced the frequency dependent
expression of conductivity and the band gap energy in $AdS_{4}$ Schwarzschild
background for p-wave holographic superconductors considering
Einstein-Yang-Mills theory. We also used the self consistent approach to obtain
the expressions of conductivity for different frequency ranges at low
temperature. We then compared the imaginary part of conductivity at low
frequency region. The band gap energy obtained from these two methods seem to
agree very well.
