Some complete monotonicity properties for the (p,q)(p,q)-gamma function

For the Γp,qΓp,q-function, we derive several properties and characteristics related to convexity, log-convexity and complete monotonicity. Similar properties and characteristics of the corresponding (p,q)(p,q)-analogue ψp,q(x)ψp,q(x) of the digamma or the ψ  -function have also been established. By applying the main results in this paper when p→∞p→∞ and q→1q→1, we obtain all of the results given in several earlier works by (for example) Krasniqi, Shabani, and other authors. Some potential areas of applications of the results presented in this paper are also indicated.