Preprint Article Version 1 This version is not peer-reviewed

Convexity Properties and Inequalities Concerning the (p,k)-Gamma function

Version 1 : Received: 10 January 2017 / Approved: 11 January 2017 / Online: 11 January 2017 (07:35:30 CET)

A peer-reviewed article of this Preprint also exists.

K. Nantomah. Convexity Properties and Inequalities Concerning the (p,k)-Gamma function. Commun. Fac. Sci. Univ. Ank. Series A1, 66(2)(2017), 130-140. DOI: 10.1501/Commua1_0000000807 K. Nantomah. Convexity Properties and Inequalities Concerning the (p,k)-Gamma function. Commun. Fac. Sci. Univ. Ank. Series A1, 66(2)(2017), 130-140. DOI: 10.1501/Commua1_0000000807

Journal reference: Communications Series A1 Mathematics & Statistics 2017
DOI: 10.1501/Commua1_0000000807

Abstract

In this paper, some convexity properties and some inequalities for the (p,k)-analogue of the Gamma function, Гp,k(x) are given. In particular, a (p,k)-analogue of the celebrated Bohr-Mollerup theorem is given. Furthermore, a (p,k)-analogue of the Riemann zeta function, ζp,k(x) is introduced and some associated inequalities are derived. The established results provide the (p,k)-generalizations of some known results concerning the classical Gamma function.

Subject Areas

(p,k)-Gamma function; convex functions; Bohr-Mollerup theorem; (p,k)-Riemann zeta function; inequality

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