Journal of Applied Mathematics

On Hermite-Hadamard Type Inequalities for $s$-Convex Functions on the Coordinates via Riemann-Liouville Fractional Integrals

Feixiang Chen

Abstract

We obtain some Hermite-Hadamard type inequalities for $s$-convex functions on the coordinates via Riemann-Liouville integrals. Some integral inequalities with the right-hand side of the fractional Hermite-Hadamard type inequality are also established.

Article information

Source
J. Appl. Math., Volume 2014 (2014), Article ID 248710, 8 pages.

Dates
First available in Project Euclid: 2 March 2015

https://projecteuclid.org/euclid.jam/1425305763

Digital Object Identifier
doi:10.1155/2014/248710

Mathematical Reviews number (MathSciNet)
MR3212492

Citation

Chen, Feixiang. On Hermite-Hadamard Type Inequalities for $s$ -Convex Functions on the Coordinates via Riemann-Liouville Fractional Integrals. J. Appl. Math. 2014 (2014), Article ID 248710, 8 pages. doi:10.1155/2014/248710. https://projecteuclid.org/euclid.jam/1425305763

References

• G. Farid, S. Abramovich, and J. Pečarić, “More about Hermite-Hadamard inequalities, Cauchy's means, and superquadracity,” Journal of Inequalities and Applications, vol. 2010, Article ID 102467, 14 pages, 2010.
• M. Bessenyei and Z. Páles, “Hadamard-type inequalities for generalized convex functions,” Mathematical Inequalities & Applications, vol. 6, no. 3, pp. 379–392, 2003.
• S. S. Dragomir and S. Fitzpatrick, “The Hadamard inequalities for $s$-convex functions in the second sense,” Demonstratio Mathematica, vol. 32, no. 4, pp. 687–696, 1999.
• S. S. Dragomir, “On the Hadamard's inequlality for convex functions on the co-ordinates in a rectangle from the plane,” Taiwanese Journal of Mathematics, vol. 5, no. 4, pp. 775–788, 2001.
• A. El Farissi, “Simple proof and refinement of Hermite-Hadamard inequality,” Journal of Mathematical Inequalities, vol. 4, no. 3, pp. 365–369, 2010.
• X. Gao, “A note on the Hermite-Hadamard inequality,” Journal of Mathematical Inequalities, vol. 4, no. 4, pp. 587–591, 2010.
• M. Z. Sarikaya, E. Set, and H. Yildirim, “On some Hadamard-type inequalities for $h$-convex functions,” Journal of Mathematical Inequalities, vol. 2, no. 3, pp. 335–341, 2008.
• H. Hudzik and L. Maligranda, “Some remarks on $s$-convex functions,” Aequationes Mathematicae, vol. 48, no. 1, pp. 100–111, 1994.
• M. Alomari and M. Darus, “The Hadamard's inequality for $s$-convex function of 2-variables on the co-ordinates,” International Journal of Mathematical Analysis, vol. 2, no. 13, pp. 629–638, 2008.
• M. Alomari and M. Darus, “Hadamard-type inequalities for $s$-convex functions,” International Mathematical Forum, vol. 3, no. 40, pp. 1965–1975, 2008.
• M. Z. Sarikaya, E. Set, H. Yaldiz, and N. Başak, “Hermite-Hadamard's inequalities for fractional integrals and related fractional inequalities,” Mathematical and Computer Modelling, vol. 57, no. 9-10, pp. 2403–2407, 2013.
• M. Z. Sar\ikaya, “On the Hermite-Hadamard-type inequalities for co-ordinated convex function via fractional integrals,” Integral Transforms and Special Functions, vol. 25, no. 2, pp. 134–147, 2014. \endinput