33B15.

In this short paper, as a complement of the double inequality on the Euler gamma function, obtained by József Sándor in the paper [A note on certain inequalities for the gamma function, J. Inequal. Pure Appl. Math., 6(3) (2000), Art. 61], several inequalities involving the Euler gamma function are established by using the same method of J. Sándor that is used in [2].