Nihonkai Mathematical Journal

On generalized Hermite-Hadamard type integral inequalities involving Riemann-Liouville fractional integrals

Mehmet Zeki Sarikaya and Hatice Yaldiz

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text


In this paper, some generalization integral inequalities of Hermite-Hadamard type for functions whose derivatives are convex in modulus are given by using fractional integrals.

Article information

Nihonkai Math. J., Volume 25, Number 2 (2014), 93-104.

First available in Project Euclid: 26 March 2015

Permanent link to this document

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 26D07: Inequalities involving other types of functions 26D10: Inequalities involving derivatives and differential and integral operators
Secondary: 26D15: Inequalities for sums, series and integrals 26A33: Fractional derivatives and integrals

Hermite-Hadamard's inequalities Riemann-Liouville fractional integral Hölder's inequality


Sarikaya, Mehmet Zeki; Yaldiz, Hatice. On generalized Hermite-Hadamard type integral inequalities involving Riemann-Liouville fractional integrals. Nihonkai Math. J. 25 (2014), no. 2, 93--104.

Export citation


  • A. G. Azpeitia, Convex functions and the Hadamard inequality, Rev. Colombiana Math. 28 (1994), 7–12.
  • M. K. Bakula and J. Pečarić, Note on some Hadamard-type inequalities, JIPAM. J. Inequal. Pure Appl. Math. 5 (2004), Article 74.
  • S. Belarbi and Z. Dahmani, On some new fractional integral inequalities, JIPAM. J. Inequal. Pure Appl. Math. 10 (2009), Article 86.
  • Z. Dahmani, New inequalities in fractional integrals, Int. J. Nonlinear Sci. 9 (2010), 493–497.
  • Z. Dahmani, On Minkowski and Hermite-Hadamard integral inequalities via fractional integration, Ann. Funct. Anal. 1 (2010), 51–58.
  • Z. Dahmani, L. Tabharit and S. Taf, Some fractional integral inequalities, Nonl. Sci. Lett. A 1 (2010), 155–160.
  • Z. Dahmani, L. Tabharit and S. Taf, New generalizations of Gruss inequality using Riemann-Liouville fractional integrals, Bull. Math. Anal. Appl. 2 (2010), 93–99.
  • J. Deng and J. Wang, Fractional Hermite-Hadamard inequalities for $(\alpha ,m)$-logarithmically convex functions, J. Inequal. Appl. 2013, Art. ID 364.
  • S. S. Dragomir and C. E. M. Pearce, Selected Topics on Hermite-Hadamard Inequalities and Applications, RGMIA Monographs, Victoria University, 2000.
  • S. S. Dragomir and R. P. Agarwal, Two inequalities for differentiable mappings and applications to special means of real numbers and to trapezoidal formula, Appl. Math. Lett. 11 (1998), 91–95.
  • R. Gorenflo and F. Mainardi, Fractional calculus: integral and differential equations of fractional order, Fractals and fractional calculus in continuum mechanics (Udine, 1996), 223–276, CISM Courses and Lectures 378, Springer, Vienna, 1997.
  • U. S. K\i rmac\i, Inequalities for differentiable mappings and applications to special means of real numbers and to midpoint formula, Appl. Math. Comp. 147 (2004), 137–146.
  • A. A. Kilbas, H. M. Srivastava and J. J. Trujillo, Theory and Applications of Fractional Differential Equations, North-Holland Mathematics Studies 204, Elsevier Sci. B.V., Amsterdam, 2006.
  • M. A. Latif, S. S. Dragomir and A. E. Matouk, New inequalities of Ostrowski type for co-ordinated convex functions via fractional integrals, J. Fract. Calc. Appl. 2 (2012), 1–15.
  • S. Miller and B. Ross, An introduction to the Fractional Calculus and Fractional Differential Equations, John Wiley & Sons, USA, 1993.
  • J. E. Pečarić, F. Proschan and Y. L. Tong, Convex Functions, Partial Orderings and Statistical Applications, Academic Press, Boston, 1992.
  • C. E. M. Pearce and J. Pečarić, Inequalities for differentiable mappings with application to special means and quadrature formulae, Appl. Math. Lett. 13 (2000), 51–55.
  • M. Z. Sarikaya and H. Yildirim, On Hermite-Hadamard type inequalities for Riemann-Liouville fractional integrals, submitted (2013).
  • M. Z. Sarikaya and H. Ogunmez, On new inequalities via Riemann-Liouville fractional integration, Abst. Appl. Anal. 2012, Art. ID 428983.
  • M.Z. Sarikaya, E. Set, H. Yaldiz and N., Basak, Hermite-Hadamard's inequalities for fractional integrals and related fractional inequalities, Math. Comput. Modelling 57 (2013), 2403–2407.
  • M. Tunc, On new inequalities for $h$-convex functions via Riemann-Liouville fractional integration, Filomat 27 (2013), 559–565.
  • Y. Zhang and J. Wang, On some new Hermite-Hadamard inequalities involving Riemann-Liouville fractional integrals, J. Inequal. Appl. 2013, Art. ID 220.