On Some Complete Monotonicity of Functions Related to Generalized k − Gamma Function

Abstract

In this paper, we presented two completely monotonic functions involving the generalized $k-$ gamma function ${\Gamma }_k\left(x\right)$ and its logarithmic derivative ${\psi }_k\left(x\right)$ , and established some upper and lower bounds for ${\mathrm{\Gamma }}_k\left(x\right)$ in terms of ${\psi }_k\left(x\right)$ .