Fractional Hermite-Hadamard Inequalities through $r$-Convex Functions via Power Means

JinRong Wang, Zeng Lin, Wei Wei

DOI Number
First page
Last page


In this paper, we firstly establish another important integralidentity for twice differentiable mapping involvingRiemann-Liouville fractional integrals. Secondly, we use thisintegral identity to derive several Riemann-Liouville fractionalHermite-Hadamard inequalities through $r$-convex functions via powermeans. Finally, some applications to quadrature formulas and specialmeans of real numbers are given.


Fractional Hermite-Hadamard inequalities, Riemann-Liouville fractional integrals, $r$-convex function, Geometric-Arithmetically $s$-convex function

Full Text:



bibitem{Kilbas} A. A. Kilbas, H. M. Srivastava, J. J. Trujillo, Theory and

applications of fractional differential equations, Elsevier Science

B.V., 2006.

bibitem{Sarikaya2} M. Z. Sarikaya, E. Set, H. Yaldiz, N. Bac{s}ak, Hermite-Hadamard's

inequalities for fractional integrals and related fractional

inequalities, Math. Comput. Model., 57(2013), 2403-2407.

bibitem{Wang-AA} J. Wang, X. Li, M. Fev{c}kan, Y. Zhou, Hermite-Hadamard-type inequalities

for Riemann-Liouville fractional integrals via two kinds of

convexity, Appl. Anal., 92(2013), 2241-2253.

bibitem{FIL1} R. Bai, F. Qi, B. Xi, Hermite-Hadamard type inequalities for the $m$-

and $(alpha, m)$-logarithmically convex functions, Filomat,

(2013), 1-7.

bibitem{FIL2} W. H. Li, F. Qi, Some Hermite-Hadamard type inequalities for functions whose $n$-th

derivatives are $(alpha, m)$-convex, Filomat, 27(2013), 1575-1582.

bibitem{Set} E. Set, New inequalities of Ostrowski type for mappings whose derivatives are

$s$-convex in the second sense via fractional integrals, Comput.

Math. Appl., 63(2012), 1147-1154.

bibitem{Zhu-JAMSI} C. Zhu, M.

Fev{c}kan, J. Wang, Fractional integral inequalities for

differentiable convex mappings and applications to special means and

a midpoint formula, J. Appl. Math. Statistics Inform., 8(2012),


bibitem{Sarikaya} M. Z. Sarikaya, On the Hermite-Hadamard-type inequalities for

co-ordinated convex function via fractional integrals, Integr.

Transf. Spec. F., 25(2014), 134-147.

bibitem{IW} I. .{I}c{s}cana, S. Wu, Hermite-Hadamard type inequalities for

harmonically convex functions via fractional integrals, Appl. Math.

Comput., 238(2014), 237-244.

bibitem{Sarikaya-11} M. Z. Sarikaya, N. Aktan, On the generalization of some integral

inequalities and their applications, Math. Comput. Model., 54(2011),


bibitem{Pearce} C. E. M. Pearce, J. Peu{c}ari'{c} and V. u{S}imi'{c}, Stolarsky

means and Hadamard's inequality, J. Math. Anal. Appl., 220(1998),


bibitem{imcompletebetafunction} A. R. DiDonato, M. P. Jarnagin, The efficient calculation of the

incomplete beta-function ratio for half-integer values of the

parameters, Math. Comp., 21(1967), 652-662.

bibitem{JIA-Deng} J. Deng, J. Wang, Fractional Hermite-Hadamard inequalities for

$(alpha,m)$-logarithmically convex functions, J. Inequal. Appl.,

(2013):34, 1-11.

bibitem{Wang-UMJ} J. Wang, J. Deng, M. Fev{c}kan, Hermite-Hadamard type inequalities

for $r$-convex functions via Riemann-Liouville fractional integrals,

Ukrainian Math. J., 65(2013), 193-211.


  • There are currently no refbacks.

© University of Niš | Created on November, 2013
ISSN 0352-9665 (Print)
ISSN 2406-047X (Online)