Ostrowski Type Fractional Integral Operator Inequalities for (m,h_1,h_2 )-Convex Functions

Jorge Eliecer Hernandez


We  establish, prove, and discuss  some new Ostrowski type inequalities for convex functions using the fractional integral operator defined by Raina R.K. in [11],  including the boundedness of the derivatives of such functions and corresponding powers. As a result of a generalization about the concept of convexity and fractional integral inequalities, these coincide, when particularized, with results for convex functions, convex functions, convex functions and others, established in other previous researches. 

Full Text:



Alomari, M. , Darus M., “Otrowski type inequalities for quasi-convex functions with applications to special means”. RGMIA Res. Rep. Coll. 13(2) , Article No. 3 (2010).

Alomari M., Darus M., Dragomir S.S., Cerone P. “Otrowski type inequalities for functions whose derivatives are s-convex in the second sense”. Appl.Math. Lett. 23, 1071-1076 (2010).

Agarwal R.P., Luo M-J., Raina R.K. “On Ostrowski type inequalities”. Fasciculli Mathematici. Nro. 56 (2016).

Breckner, W.W. 1978. Stetigkeitsaussagen für eine Klasse verallgemeinerter konvexer funktionen in topologischen linearen R¨aumen. Pub. Inst. Math., 23,13-20

Bombardelli M., Varošanec S. “Properties of h-convex functions related to the Hermite-Hadamard-Fejér inequalities”. Computers and Mathematics with Applications. Vol. 58, Issue 9, 2009, pp 1869-1877

Cerone P., Dragomir S.S., “Ostrowski type inequalities for functions whose derivative satisfy certain convexity assumptions”, Demonstr. Math. 37(2) , 299-308 (2004)

Cristescu, G.,Gaianu M., Uzair A.M. “Regularity properties and integral inequalities related to (k,h_1,h_2 )-convexity of functions”. Annalele Univeritatii de Vest, Timisoara. Seria Matematica – Informatica. 53 (1) (2015) , 19 -35.

Cristescu, G. “Weighted inequalities for Katugampola fractional integral within the class of (h_1,h_2 )-convex functions”. ISREIE (2016), 22-29. ISN 2065 2469.

Dragomir S.S.,Agarwal R.P. “Some Inequalities of Hadamard Type”. Soochow J. Math. 21 (1995).

Grinalatt M., Linnainmaa J.T. “Jensen’s Inequality, parameter uncertainty and multiperiod investment”. Review of Asset Pricing Studies. 1 (1) (2011), 1-34.

Latiff, M. A., Alomari, M. “On Hadmard-Type Inequalities for h-Convex Functions on the Co-ordinates”. Int. Journal of Math. Analysis, Vol. 3 (2009), no. 33, 1645 – 1656

Liu W., Wen W., Park J. “Hermite-Hadamard type Inequalities for MT-convex functions via classical integrals and fractional integrals”. J. Nonlinear Sci.Appl.,9 (2016),766-777.

Maksa G., Palés Z.S. “The Equality case in some recent convexity inequalities”. Opuscula Math. Vol. 31 (2), 2011, 269-277.

Ostrowski A., “Über die Absolutabweichung einer di_erentiebaren Funktion von ihrem Integralmittelwert”. Comment. Math. Helv., 10(1938), 226-227

Park J. “Some Hermite-Hadamard Type Inequalities for MT-convex functions via Classical and Riemann-Liouville fractional integrals”. Applied Mathematical Sciences. Vol 9. Nro. 101, 2015, 5011-5026.

Raina R.K. “On generalized Wright’s Hypergeometric functions and fractional Calculus Operator”. East Asian Mathematical Journal. Vol. 21,Nro. 2 (2005), 191-203.

Ruel J.J., Ayres M.P. “Jensen’s inequality predicts effects of environmental variations”. Trends in Ecology and Evolution. 14 (9) (1999), 361-366.

Sarikaya M.Z., Filiz H., Kiris M.E. “On some generalized integral inequalities for Riemann Liouville Fractional Integral”. Filomat. 29:6 (2015) 1307-1314.

Set E., “New inequalities of Ostrowski type for mapping whose derivatives are s-convex in the second sense via fractional integrals”. Comput. Math. Appl., 63(2012), 1147-1154

Shi D-P., Xi B-Y., Qi F. “Hermite-Hadamard Type Inequalities for (m,h_1,h_2 )-convex functions via Riemann-Liouville fractional integral”. Turkish Journal of Analysis and Number Theory. Vol. 2 , Nro. 1, 2014, 23-28

G. Toader, “Some generalizations of the convexity”, Proceedings of the Colloquium on Approximation and Optimization, Univ. Cluj-Napoca, Cluj-Napoca, 1985, 329-338.

M. Tunç¸,” Ostrowski type inequalities via h-convex functions with applications to special means”, Journal of Inequalities and Applications 2013, 2013:326

Varošanec S. “On h-convexity”. J. Math. Anal. Appl. 326 (2007) , 303-311.

Vivas C. M., García C. “Ostrowski type inequalities for functions whose derivatives are (m,h_1,h_2 )-convex”. Applied Mathematics and Information Science. Vol. 11 (1). (2017).

Xi B-Y., Qi F. “Properties and inequalities for the (h_1,h_2 )- and (h_1,h_2,m)-GA-convex functions”. Cogent Mathematics, (2016), 3: 1176620


  • There are currently no refbacks.

MAYFEB Journal of Mathematics 
Toronto, Ontario, Canada
ISSN 2371-6193