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

Mehmet Zeki Sarikaya^1, 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

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

Abstract

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.

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

This 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/

References:

[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.