Turkish Journal of Analysis and Number Theory
ISSN (Print): 2333-1100 ISSN (Online): 2333-1232 Website: http://www.sciepub.com/journal/tjant
Open Access
Journal Browser
Turkish Journal of Analysis and Number Theory. 2014, 2(3), 85-89
DOI: 10.12691/tjant-2-3-6
Open AccessArticle

On The Hermite- Hadamard-Fejér Type Integral Inequality for Convex Function

Mehmet Zeki Sarikaya1, and Samet Erden2

1Department of Mathematics, Faculty of Science and Arts, Düzce University, Konu-ralp Campus, Düzce-TURKEY

2Department of Mathematics, Faculty of Science, Bartn University, Konuralp Cam-pus, BARTIN-TURKEY

Pub. Date: July 03, 2014

Cite this paper:
Mehmet Zeki Sarikaya and Samet Erden. On The Hermite- Hadamard-Fejér Type Integral Inequality for Convex Function. Turkish Journal of Analysis and Number Theory. 2014; 2(3):85-89. doi: 10.12691/tjant-2-3-6


In this paper, we extend some estimates of the right hand side of a Hermite- Hadamard-Fejér type inequality for functions whose first derivatives absolute values are convex. The results presented here would provide extensions of those given in earlier works.

Ostrowski’s inequality Montgomery’s identities convex function Hölder inequality

Creative CommonsThis work is licensed under a Creative Commons Attribution 4.0 International License. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/


[1]  Z. Dahmani, On Minkowski and Hermite-Hadamard integral inequalities via fractional integration, Ann. Funct. Anal. 1 (1) (2010), 51-58.
[2]  J. Deng and J. Wang, Fractional Hermite-Hadamard inequalities for (α; m)-logarithmically convex functions.
[3]  S. S. Dragomir and R.P. Agarwal, Two inequalities for differentiable mappings and applications to special means of real numbers and to trapezoidal formula, Appl. Math. lett., 11 (5) (1998), 91-95.
[4]  S. S. Dragomir and C. E. M. Pearce, Selected Topics on Hermite-Hadamard Inequalities and Applications, RGMIA Monographs, Victoria University, 2000.
[5]  S. Hussain, M.A. Latif and M. Alomari, Generalized duble-integral Ostrowski type inequalities on time scales, Appl. Math. Letters, 24 (2011), 1461-1467.
[6]  M. E. Kiris and M. Z. Sarikaya, On the new generalization of Ostrowski type inequality for double integrals, International Journal of Modern Mathematical Sciences, 2014, 9 (3): 221-229.
[7]  L. Fejer, Über die Fourierreihen, II. Math. Naturwiss. Anz Ungar. Akad. Wiss., 24 (1906), 369.390. (Hungarian).
[8]  I. I, scan, Hermite-Hadamard-Fejer type inequalities for convex functions via fractional integrals, arXiv preprint arXiv: 1404. 7722 (2014).
[9]  U.S. Krmac, Inequalities for dif ferentiable mappings and applications to special means of real numbers and to midpoint formula, Appl. Math. Comp., 147 (2004), 137-146.
[10]  J. Peµcari´c, F. Proschan and Y.L. Tong, Convex functions, partial ordering and statistical applications, Academic Press, New York, 1991.
[11]  M. Z. Sarikaya, E. Set, H. Yaldiz and N., Basak, Hermite -Hadamard.s inequalities for fractional integrals and related fractional inequalities, Mathematical and Computer Modelling, 57 (2013) 2403. 2407.
[12]  M. Z. Sarikaya and H. Yildirim, On Hermite-Hadamard type inequalities for Riemann- Liouville fractional integrals, Submited
[13]  M. Z. Sarikaya, On new Hermite Hadamard Fejer Type integral inequalities, Studia Universitatis Babes-Bolyai Mathematica., 57 (2012), No. 3, 377-386.
[14]  K-L. Tseng, G-S. Yang and K-C. Hsu, Some inequalities for differentiable mappings and applications to Fejer inequality and weighted trapozidal formula, Taiwanese J. Math. 15 (4), pp: 1737-1747, 2011.
[15]  C.-L. Wang, X.-H. Wang, On an extension of Hadamard inequality for convex functions, Chin. Ann. Math. 3 (1982) 567. 570.
[16]  S.-H. Wu, On the weighted generalization of the Hermite-Hadamard inequality and its applications, The Rocky Mountain J. of Math., vol. 39, no. 5, pp. 1741. 1749, 2009.
[17]  M. Tunc, On new inequalities for h-convex functions via Riemann-Liouville fractional integration, Filomat 27: 4 (2013), 559. 565.
[18]  J. Wang, X. Li, M. Feckan and Y. Zhou, Hermite-Hadamard-type inequalities for Riemann-Liouville fractional integrals via two kinds of convexity, Appl. Anal. (2012).
[19]  B-Y, Xi and F. Qi, Some Hermite-Hadamard type inequalities for differentiable convex func- tions and applications, Hacet. J. Math. Stat. 42 (3), 243. 257 (2013).
[20]  B-Y, Xi and F. Qi, Hermite-Hadamard type inequalities for functions whose derivatives are of convexities, Nonlinear Funct. Anal. Appl. 18 (2), 163. 176 (2013).
[21]  Y. Zhang and J-R. Wang, On some new Hermite-Hadamard inequalities involving Riemann-Liouville fractional integrals, Journal of Inequalities and Applications 2013, 2013: 220.