Skip to main content
Log in

    We’re sorry, something doesn't seem to be working properly.

    Please try refreshing the page. If that doesn't work, please contact support so we can address the problem.

Abstract

In this paper, we have established some generalized Simpson type integral inequalities for generalized fractional integral. The results presented here would provide some fractional inequalities involving k-fractional integral and Riemann–Liouville type fractional operators.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Alomari, M., Darus, M., Dragomir, S.S.: New inequalities of Simpsonís type for \(s\)-convex functions with applications. RGMIA Res Rep Coll 12(4); (2009) (Article 9)

  2. Chen, J., Huang, X.: Some new inequalities of Simpson’s type for \(s\)-convex functions via fractional integrals. Filomat 31(15), 4989–4997 (2017)

    Article  MathSciNet  Google Scholar 

  3. Dragomir, S.S., Agarwal, R.P., Cerone, P.: On Simpsonís inequality and applications. J. Inequal. Appl. 5, 533–579 (2000)

    MathSciNet  MATH  Google Scholar 

  4. Dragomir, S.S.: On Simpson’s quadrature formula for differentiable mappings whose derivatives belong to \(l_{p}\) spaces and applications. J. KSIAM 2, 57–65 (1998)

    Google Scholar 

  5. Dragomir, S.S.: On Simpson’s quadrature formula for Lipschitzian mappings and applications Soochow. J. Math. 25, 175–180 (1999)

    MathSciNet  MATH  Google Scholar 

  6. Du, T., Li, Y., Yang, Z.: A generalization of Simpson’s inequality via differentiable mapping using extended \((s, m)\) -convex functions. Appl. Math Comput. 293, 358–369 (2017)

    MathSciNet  MATH  Google Scholar 

  7. Hussain, S., Qaisar, S.: More results on Simpson’s type inequality through convexity for twice differentiable continuous mappings, vol. 5. Springer, Berlin, pp 77 (2016)

  8. Liu, B.Z.: An inequality of Simpson type. Proc. R. Soc. A 461, 2155–2158 (2005)

    Article  MathSciNet  Google Scholar 

  9. Mubeen, S., Habibullah, G.M.: k-Fractional integrals and application. Int. J. Contemp. Math. Sci. 7(2), 89–94 (2012)

    MathSciNet  MATH  Google Scholar 

  10. Pecaric, J., Proschan, F., Tong, Y.L.: Convex functions, partial ordering and statistical applications. Academic Press, New York (1991)

    Google Scholar 

  11. Pecaric, J., Varosanec, S.: A note on Simpson’s inequality for functions of bounded variation. Tamkang J. Math. 31(3), 239–242 (2000)

  12. Qaisar, S., He, C.J., Hussain, S.: A generalizations of Simpson’s type inequality for differentiable functions using \((\alpha ,m) \)-convex functions and applications. J. Inequal. Appl. 13 (2013) (Article 158)

  13. Kavurmaci, H., Akdemir, A.O., Set, E., Sarikaya, M.Z.: Simpson’s type inequalities for \(m\)-and \((\alpha, m)\) -geometrically convex functions. Konuralp J. Math. 2(1), 90–101 (2014)

    MATH  Google Scholar 

  14. Ozdemir, M.E., Akdemir, A.O., Kavurmacı, H.: On the Simpson’s inequality for convex functions on the co-ordinates. Turk. J. Anal. Number Theory 2(5), 165–169 (2014)

    Article  Google Scholar 

  15. Sarıkaya, M. Z., Ertuğral, F.: On the generalized Hermite-Hadamard inequalities 2017 (submitted)

  16. Sarikaya, M.Z., Set, E., Ozdemir, M.E.: On new inequalities of Simpson’s type for \(s\)-convex functions. Comput. Math. Appl. 60, 2191–2199 (2010)

    Article  MathSciNet  Google Scholar 

  17. Sarikaya, M.Z., Set, E., Özdemir, M.E.: On new inequalities of Simpson’s type for convex functions. RGMIA Res. Rep. Coll. 13(2) (2010) (Article 2)

  18. Sarikaya, M.Z., Set, E., Ozdemir, M.E.: On new inequalities of Simpson’s type for functions whose second derivatives absolute values are convex. J. Appl. Math. Stat. Inf. 9(1) (2013)

  19. Sarıkaya, M.Z., Tunç, T., Budak, H.: Simpson’s type inequality for \(F\)-convex function. Facta Universitatis Ser. Math. Inform. (in press)

  20. Set, E., Ozdemir, M.E., Sarikaya, M.Z.: On new inequalities of Simpson’s type for quasi-convex functions with applications. Tamkang J. Math. 43(3), 357–364 (2012)

    Article  MathSciNet  Google Scholar 

  21. Set, E., Sarikaya, M. Z., Uygun, N.: On new inequalities of Simpson’s type for generalized quasi-convex functions. Adv. Inequal. Appl. 3, 1–11 (2017)

  22. Tseng, K.L., Yang, G.S., Dragomir, S.S.: On weighted Simpson type inequalities and applications. J. Math. Inequal. 1(1), 13–22 (2007)

    Article  MathSciNet  Google Scholar 

  23. Ujevic, N.: Double integral inequalities of Simpson type and applications. J. Appl. Math. Comput. 14(1–2), 213–223 (2004)

    Article  MathSciNet  Google Scholar 

  24. Yang, Z.Q., Li, Y.J., Du, T.: A generalization of Simpson type inequality via differentiable functions using (\(s, m\) )-convex functions. Ital. J. Pure Appl. Math. 35, 327–338 (2015)

    MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Fatma Ertuğral.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Ertuğral, F., Sarikaya, M.Z. Simpson type integral inequalities for generalized fractional integral. RACSAM 113, 3115–3124 (2019). https://doi.org/10.1007/s13398-019-00680-x

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s13398-019-00680-x

Keywords

Mathematics Subject Classification

Navigation