Research Article
New Integral Inequalities in Quantum Calculus
- Faculty of sciences of Tunis, TUNISIA
* Corresponding author
Abstract
In this paper, we study the q-analogue of Klamkin-McLenaghan's and Grueb-Reinboldt's inequalities then we use the Riemann-Liouville fractional q-integral to get some new integral results.
How to Cite
K. Brahim, S. Taf, B. Nefzi, New Integral Inequalities in Quantum Calculus, Int. J. Anal. Appl. 7 (2015), 50–58.
BibTeX
@article{Brahim2015,
author = {Brahim, Kamel and Taf, Sabrina and Nefzi, Bochra},
title = {New Integral Inequalities in Quantum Calculus},
journal = {Int. J. Anal. Appl.},
volume = {7},
year = {2015},
pages = {50--58},
doi = {}
}References
- [1] Anber. A and Dahmani. Z., New integral results using P ´olya-Szeg ¨o inequalities, ACTA et Comm. Univ. Tari de Math. 17 (2) (2013), 171-178.
- [2] Brahim. K and Taf. S., On some fractional q-integral inequalities, Malaya Journal of Matematik 3(1)(2013), 21-26.
- [3] Brahim. K and Taf. S., Some Fracional Intehral Inequalities In Quantum Calculus, Journal of Fractional Calculus and Application. 4(2)(2013), 245-250.
- [4] Dahmani. Z., Tabahrit. L and Taf.S., New generalisation of Gr ¨uss inequality using RiemannLiouville fractional integrals, Bull. Math. Anal. Appl. 2(2010), 93-99.
- [5] Dragomir. S.S., Some integral inequalities of Gr ¨uss type, Indian J.Pure Apll. Math. 31(2000),397-415.
- [6] Dragomir. S.S. and Diamond. N.T., Integral inequalities of Gr ¨uss type via P ´olya-Szeg ¨o and Shisha-Mond results,East Asian Math. J.19 (2003), 27-39.
- [7] Gasper. G and Rahman. R., Basic Hypergeometric Series, 2nd Edition, (2004), Encyclopedia of Mathematics and Its Applications, 96, Cambridge University Press, Cambridge.
- [8] Gauchman. H., Integral inequalities in q-calculus, Comput. Math. Appl. 47 (2-3)(2004), 281- 300.
- [9] Grueb. W and Rheinboldt. W., On generalisation of an inequality of L.V. Kantrovich, Proc. Amer. Math. Soc., 10 (1959), 407-415.
- [10] Gr ¨uss. G., Uber das maximum des absoluten Betrages von 1/(b - a) R b a f(x)g(x)dx - 1/(b - a) 2 R b a f(x)dx R b a g(x)dx, Math.Z.39(1)(1935), 215-226.
- [11] Jackson. F.H., On a q-Definite Integrals. Quarterly Journal of Pure and Applied Mathematics 41, 1910, 193-203.
- [12] Klamkin. D.S and McLenaghan. J.E., An ellipse inequality, Math. Mag., 50 (1977), 261-263.
- [13] Kac. V.G and Cheung. P., Quantum Calculus, Universitext, Springer-Verlag, New York, (2002).
- [14] Mercer. A.McD and Mercer. P., New proofs of the Gr ¨uss inequality, Aust. J. Math. Anal. Apll. 1 (2) (2004), Article ID 12.
- [15] Mitrinovi ´c. D.S., Peˇcari ´c. J.E., Fink. A.M., Classical and New Inequalities in Analysis, in: Mathematics and its Applications, Vol. 61, Kluwer Acadmic Publishers, Dordrecht, The Netherlands, 1993.
- [16] Rajkovi ´c. P.M and Marinkonvi ´c. S.D., Fractional integrals and derivatives in q-calculus, Applicable analysis and discrete mathematics, 1 (2007), 311-323.
- [17] Rajkovi ´c. P., Marinkonvi ´c. S.D and Stankovi ´c. M.S., The inequalities for some types of qintegrals, ArXiv. Math. CA, 8 May 2006.
- [18] Sarikaya. M.Z, Aktan. N and Yildirim. H., On weighted Cebyˇsev-Gr ¨uss type inequalities on ˇ time scales, J. Math. Inequal. 2(2008), 185-195.