Title: New Integral Inequalities in Quantum Calculus
Author(s): Kamel Brahim, Sabrina Taf, Bochra Nefzi
Pages: 50-58
Cite as:
Kamel Brahim, Sabrina Taf, Bochra Nefzi, New Integral Inequalities in Quantum Calculus, Int. J. Anal. Appl., 7 (1) (2015), 50-58.


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.

Full Text: PDF



  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.