Some monotonicity properties and inequalities for Γ and ζ - functions

Valmir Krasniqi, Toufik Mansour, Armend Sh Shabani

Research output: Contribution to journalArticlepeer-review


In this paper several monotonicity properties and inequalities are given for Γ and Γq functions as well as for their logarithmic derivatives ψ and ψq A p analogue of Riemann Zeta function ζp is introduced. Using the generalization of Schwarz inequality and Holder's inequality some inequalities relating ζ, ζp, Γ and Γp 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 Γp-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.

Original languageEnglish
Pages (from-to)365-376
Number of pages12
JournalMathematical Communications
Issue number2
StatePublished - Dec 2010


  • Gamma function
  • Psi function
  • Zeta function

ASJC Scopus subject areas

  • Analysis
  • Algebra and Number Theory
  • Geometry and Topology
  • Applied Mathematics


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