Some monotonicity properties and inequalities for $Gamma$ and $zeta$ - functions

In this paper several monotonicity properties and inequalities are given for $Gamma$ and $Gamma_q$ functions as well as for their logarithmic derivatives $psi$ and $psi_q$. A $p$ analogue of Riemann Zeta function $zeta_p$ is introduced. Using the generalization of Schwarz inequality and Holder\u27s inequality some inequalities relating $zeta, zeta_p, Gamma$ and $Gamma_p$ are obtained. By the use of Laplace Convolution Theorem, some monotonicity results related to digamma function $psi$ and its derivatives of order $n$ are obtained. For the $Gamma_p$-function, defined by Euler, some properties related to monotonicity are given. Also, some properties of a $p$ analogue of the $psi$ function have been established