Some inequalities for the q,k-Gamma and Beta functions

Downloads

DOI:

https://doi.org/10.26637/mjm201/008

Abstract

Using q-integral inequalities we establish some new inequalities for the qk Gamma, Beta and Psi functions.

Keywords:

q,k-Gamma, q,k-Beta, q-integral inequalities

Mathematics Subject Classification:

33D05, 33D60, 41A17
  • Kamel Brahim Institut Supérieur des ´ Etudes Préparatoires en Biologie et Géologie de la Soukra, Tunisia.
  • Yosr sidomou Institut Supérieur des ´ Etudes Préparatoires en Biologie et Géologie de la Soukra, Tunisia.
  • Pages: 61-71
  • Date Published: 01-01-2014
  • Vol. 2 No. 01 (2014): Malaya Journal of Matematik (MJM)

R. Diaz, C. Teruel, q,k-Generalized Gamma and Beta Functions, Journal of Nonlinear Mathematical Physics, Volume 12, Number 1 (2005), 118-134. DOI: https://doi.org/10.2991/jnmp.2005.12.1.10

S. S. Dragomir, R. P. Agarwal, and N. S. Barnett, Inequality for Beta and Gamma functions via some classical and new integral inequalities, J. Inequal., 5(2)(2000), 103-165. DOI: https://doi.org/10.1155/S1025583400000084

A. Fitouhi, K. Brahim, Some inequalities for the q-Beta and the q-Gamma functions via some q-integral inequalities , Applied Mathematics and computation, 204(2008), 385-394. DOI: https://doi.org/10.1016/j.amc.2008.06.055

G. Gasper and M. Rahman, Basic Hypergeometric Series, Encyclopedia of Mathematics and its Application, Vol 35 Cambridge Univ. Press, Cambridge, UK, 1990.

H. Gauchman, Integral Inequalities in q-Calculus, Computers and Mathematics with Applications, 47(2004), 281-300. DOI: https://doi.org/10.1016/S0898-1221(04)90025-9

F. H. Jackson, A generalization of the function Γ(n) and x n , Proc. Roy. Soc. London, (74)(1904), 64-72.

F. H. Jackson, On a q-Definite Integrals, Quarterly Journal of Pure and Applied Mathematics, 41(1910), 193-203.

V. G. Kac and P. Cheung, Quantum Calculus, Universitext, Springer-Verlag, New York, (2002). DOI: https://doi.org/10.1007/978-1-4613-0071-7

T. H. Koornwinder, q-Special Functions, a Tutorial, in Deformation theory and quantum groups with applications to mathematical physics, M. Gerstenhaber and J. Stasheff (eds), Contemp. Math. 134, Amer.Math. Soc., (1992).

T. H. Koornwinder, Special Functions and q-Commuting Variables, in Special Functions, q-Series and related Topics, M. E. H. Ismail, D. R. Masson and M. Rahman (eds), Fields Institute Communications 14,

American Mathematical Society, (1997), pp. 131–166; arXiv:q-alg/9608008.

J. Thomae, Beitrage zur Theorie der durch die Heinesche Reihe, J. reine angew. Math., (70)(1869), 258-281. DOI: https://doi.org/10.1515/9783112389409-021

  • NA

Metrics

PDF views
71
Jan 2014Jul 2014Jan 2015Jul 2015Jan 2016Jul 2016Jan 2017Jul 2017Jan 2018Jul 2018Jan 2019Jul 2019Jan 2020Jul 2020Jan 2021Jul 2021Jan 2022Jul 2022Jan 2023Jul 2023Jan 2024Jul 2024Jan 2025Jul 2025Jan 20267.0
|

Published

01-01-2014

How to Cite

Kamel Brahim, and Yosr sidomou. “Some Inequalities for the q,k-Gamma and Beta Functions”. Malaya Journal of Matematik, vol. 2, no. 01, Jan. 2014, pp. 61-71, doi:10.26637/mjm201/008.