Convexity Properties and Inequalities Concerning the (p,k)-Gamma function

In this paper, some convexity properties and some inequalities for the (p,k)-analogue of the Gamma function, Гp,k(x) are given. In particular, a (p,k)-analogue of the celebrated Bohr-Mollerup theorem is given. Furthermore, a (p,k)-analogue of the Riemann zeta function, ζp,k(x) is introduced and some associated inequalities are derived. The established results provide the (p,k)-generalizations of some known results concerning the classical Gamma function.