APPLIED JOURNAL OF PHYSICAL SCIENCE
Integrity Research Journals
ISSN: 2756-6684
Model: Open Access/Peer Reviewed
DOI: 10.31248/AJPS
Start Year: 2018
Email: ajps@integrityresjournals.org
Convexity properties and inequalities regarding the q-Gamma function
https://doi.org/10.31248/AJPS2022.084 | Article Number: 4FF3C3A81 | Vol.4 (4) - December 2022
Received Date: 09 November 2022 | Accepted Date: 13 December 2022 | Published Date: 30 December 2022
Authors: Hashimu, Mohammed* , Abdul Razak Yaabia Abdulai and Hatsu Edo
Keywords: Convex function, Gamma function, q-analogue of exponential function, q-analogue of gamma function, psi function, logarithmically convex.
This paper is motivated by the work of K. Nantomah in 2017. In the paper, some convexity properties and some inequalities for the (p, k)-analogue of the Gamma function, were given. The method engaged in displaying the result makes use of the (p, k)-analogue of the Gamma function. In addition, H der’s integral inequality, Young’s inequality and some basic definitions of a convex function were used. As a result, the (p, k)-generalization of some known outcomes concerning the classical gamma function was specified. The fundamental objective of this paper is to ascertain some convexity properties and some inequalities regarding the q-analogue of the Gamma function, . First, utilizing similar techniques as K. Nantomah, the convexity property of the q-Gamma function was demonstrated. Next, exploiting Young’s inequality, some inequalities regarding the q-Gamma function were substantiated. At the end, the q-analogue of some accepted results concerning the classical Gamma function was proven.
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