On the Hermite-Hadamard-Fejer-type inequalities for co-ordinated convex functions via fractional integrals

Hatice Yaldız, Mehmet Zeki Sarıkaya, Zoubir Dahmani


In this paper, using Riemann-Liouville integral operators, we establish new fractional in- tegral inequalities of Hermite-Hadamard-Fejer type for co-ordinated convex functions on a rectangle of R^2. The results presented here would provide extensions of those given in earlier works. 


Riemann-Liouville fractional integrals, convex function, co-ordinated convex mapping and Hermite-Hadamard-Fejer inequality.

Full Text:



Alomari, M., Darus, M., Co-ordinated s- convex function in the first sense with some Hadamard-type inequalities, Int. J.

Contemp. Math. Sciences, 3 (32),1557-1567 (2008).

Alomari, M., Darus, M., On the Hadamard’s inequality for log-convex functions on the co- ordinates, J. of Inequal. and Appl, Article ID 283147, 13 pages,(2009).

Alomari, M., Darus, M., Fejer inequality for double integrals, Facta Universitatis (Nis) Ser. Math. Inform., 24 , 15-28(2009).

Kilbas, A.A., Srivastava H.M., Trujillo, J.J., Theory and Applications of Fractional Differ- ential Equations, North-Holland Mathemat- ics Studies, 204, Elsevier Sci. B.V., Amster- dam, (2006).

Belarbi, S., Dahmani, Z., On some new frac- tional integral inequalities, J. Ineq. Pure and Appl. Math., 10(3) , Art. 86, (2009). [6] Dahmani, Z., New inequalities in fractional integrals, International Journal of Nonlinear Scinece, 9(4) , 493-497, (2010).

Dahmani, Z., On Minkowski and Hermite- Hadamard integral inequalities via fractional integration, Ann. Funct. Anal. 1(1), 51-58, (2010).

Dahmani, Z., Tabharit, L., Taf, S., Some fractional integral inequalities, Nonl. Sci. Lett. A, 1(2) , 155-160, (2010).

Dahmani, Z., Tabharit, L., Taf, S., New generalizations of Gru ̈ss inequality usin Riemann-Liouville fractional integrals, Bull. Math. Anal. Appl., 2(3) , 93-99, (2010).

Dragomir, S.S., On Hadamard’s inequality for convex functions on the co-ordinates in arectangle from the plane, Taiwanese Jour- nal of Mathematics, 4, 775-788, (2001).

Fej ́er, L., Uberdie Fourierreihen, II, Math. Naturwise. Anz Ungar. Akad., Wiss, 24, 369- 390(1906), (in Hungarian).

Gorenflo, R., Mainardi, F., Fractional cal- culus: integral and differential equations of fractional order, Springer Verlag, Wien, 223- 276, (1997).

Hadamard, J., Etude sur les proprietes des fonctions entieres et en particulier d’une fonc- tion considree par, Riemann, J. Math. Pures. et Appl. 58, 171–215,(1893).

Iscan, I., Hermite-Hadamard-Fejer type in- equalities for convex functions via fractional integrals, 2014, arXiv:1404.7722v1.

Latif, M.A., Alomari, M., Hadamard-type inequalities for product two convex functions on the co-ordinetes, Int. Math. Forum, 4(47), 2327-2338,(2009).

Latif, M.A., Alomari, M., On the Hadamard-type inequalities for h-convex functions on the co-ordinetes, Int. J. of

Math. Analysis, 3(33), 1645-1656,(2009).

Latif, M.A., Hussain, S., New inequalities of Ostrowski type for co-ordineted convex func- tions via fractional integrals, Journal of Frac- tional Calculus and Applications,Vol. 2, No.

, pp. 1-15, (2012).

Miller, S., Ross, B., An introduction to the

fractional calculus and fractional differential equations, John Wiley & Sons, USA, p.2, (1993).

Minculete, N., Mitroi, F-C.,Fejer-type in- equalities, Aust. J. Math. Anal. Appl. 9, no. 1, Art. 12, 8pp,(2012).

Ozdemir,M.E.,Set,E.,Sarikaya,M.Z.,New some Hadamard’s type inequalities for co- ordinated m-convex and (α, m)-convex func- tions, Hacettepe Journal of Mathematics and Statistics , 40(2), 219-229, (2011).

Sarikaya, M.Z., On new Hermite Hadamard Fej ́er type integral inequalities, Stud. Univ. Babe ̧s-Bolyai Math. 57 (3), 377–386, (2012).

Sarikaya, M.Z., Set, E., Ozdemir M.E., Dragomir, S.S., New some Hadamard’s type inequalities for co-ordinated convex func- tions, Tamsui Oxford Journal of Informa- tion and Mathematical Sciences, 28(2),137- 152, (2012) .

Sarikaya M.Z., Ogunmez, H., On new in- equalities via Riemann-Liouville fractional integration, Abstract and Applied Analysis, Volume 2012, Article ID 428983, 10 pages, doi:10.1155/2012/428983.

Sarikaya, M.Z., Set, E., Yaldiz, H., Basak, N., Hermite-Hadamard’s inequalities for fractional integrals and related fractional inequalities, Mathematical and Computer Modelling, 57, 2403–2407,(2013).

Sarikaya, M.Z., Ostrowski type inequalities involving the right Caputo fractional deriva- tives belong to Lp, Facta Universitatis, Series Mathematics and Informatics , Vol. 27 No 2, 191-197, (2012).

Sarikaya, M.Z., Yaldiz, H., On weighted Montogomery identities for Riemann- Liouville fractional integrals, Konuralp Journal of Mathematics, Volume 1 No. 1 pp. 48-53, (2013).

Sarikaya, M.Z., Yaldiz, H., On the Hadamard’s type inequalities for L- Lipschitzian mapping, Konuralp Journal of Mathematics, Volume 1 No. 2 pp. 33–40 (2013).

Sarikaya, M.Z., On the Hermite–Hadamard- type inequalities for co-ordinated convex function via fractional integrals, Integral

Transforms and Special Functions, Vol. 25, No. 2, 134–147, (2014).

DOI: http://dx.doi.org/10.11121/ijocta.01.2017.00405


  • There are currently no refbacks.

Copyright (c) 2017 Hatice YALDIZ, Mehmet Zeki SARIKAYA, Zoubir DAHMANI

Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.


   ithe_170     crossref_284         ind_131_43_x_117_117  logo_ehost_120    ulakbim_140   proquest_256_x_97_256   zbmath_251_x_86_251 more...