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

JinRong Wang, Zeng Lin, Wei Wei

DOI Number
-
First page
129
Last page
145

Abstract


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.

Keywords


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

Full Text:

PDF

References


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),

-28.

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),

-2182.

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),

-109.

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.


Refbacks

  • There are currently no refbacks.




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