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

In this paper several monotonicity properties and inequalities are given for Γ and Γ_q functions as well as for their logarithmic derivatives ψ and ψ_q A p analogue of Riemann Zeta function ζ_p is introduced. Using the generalization of Schwarz inequality and Holder's inequality some inequalities relating ζ, ζ_p, Γ and Γ_p are obtained. By the use of Laplace Convolution Theorem, some monotonicity results related to digamma function ψ and its derivatives of order n are obtained. For the Γ_p-function, defined by Euler, some properties related to monotonicity are given. Also, some properties of a p analogue of the ψ function have been established.