New Integral Inequalities in Quantum Calculus

Article Sidebar

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

Main Article Content

Kamel Brahim, Sabrina Taf, Bochra Nefzi

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.

Article Details

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.