Turkish Journal of Analysis and Number Theory
ISSN (Print): 2333-1100 ISSN (Online): 2333-1232 Website: http://www.sciepub.com/journal/tjant
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Turkish Journal of Analysis and Number Theory. 2017, 5(3), 117-120
DOI: 10.12691/tjant-5-3-5
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Some Integral Inequalities of Hermite-Hadamard Type for ε-convex Functions

Jun Zhang1, Zhi-Li Pei1 and Feng Qi2, 3,

1College of Computer Science and Technology, Inner Mongolia University for Nationalities, Tongliao City 028043, Inner Mongolia Autonomous Region, China

2School of Mathematics and Informatics, Henan Polytechnic University, Jiaozuo City, Henan Province, 454010, China,

3Department of Mathematics, School of Science, Tianjin Polytechnic University, Tianjin City, 300387, China

Pub. Date: May 19, 2017

Cite this paper:
Jun Zhang, Zhi-Li Pei and Feng Qi. Some Integral Inequalities of Hermite-Hadamard Type for ε-convex Functions. Turkish Journal of Analysis and Number Theory. 2017; 5(3):117-120. doi: 10.12691/tjant-5-3-5


In the paper, the authors establish a new integral identity. By this integral identity and Hölder’s inequality, the authors obtain some new inequalities of the Hermite-Hadamard type for ε-convex functions.

Hermite-Hadamard type type inequality Integral identity ε-convex function

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[1]  D. H. Hyers, S. M. Ulam, Approximately convex functions, Proc. Amer. Math. Soc., 3 (1952), 821-828.
[2]  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(1998), 91-95.
[3]  C. E. M. Pearce and J. Pečarić, Inequalities for differentiable mappings with application to special means and quadrature formula. Appl. Math. Lett., 13(2000), 51–55.
[4]  F. Qi and B.-Y. Xi, Some Hermite–Hadamard type inequalities for geometrically quasi-convex functions, Proceedings of the Indian Academy of Sciences (Mathematical Sciences), 124:3(2014), 333-342.
[5]  F. Qi, T.-Y. Zhang, and B.-Y. Xi, Integral inequalities of Hermite-Hadamard type for functions whose first derivatives are of convexity, Ukrainian Mathematical Journal, 66:5(2015), 625-640.
[6]  B.-Y. Xi, R.-F. Bai, and F. Qi, Hermite-Hadamard type inequalities for the m- and (α,m)-geometrically convex functions, Aequationes Math., 184:3(2012), 261-269.
[7]  B.-Y. Xi and F. Qi, Hermite-Hadamard type inequalities for geometrically r-convex functions, Studia Scientiarum Mathematicarum Hungarica, 51:4(2014), 530-546;.
[8]  B.-Y. Xi and F. Qi, Inequalities of Hermite-Hadamard type for extended s-convex functions and applications to means, J. Nonlinear Convex Anal,. 16(2015), 873-890.
[9]  B.-Y. Xi, S.-H. Wang, and F. Qi, Some inequalities for (h,m)-convex functions, Journal of Inequalities and Applications, 2014, 100, 12~pages.
[10]  B.-Y. Xi, T.-Y. Zhang, and F. Qi, Some inequalities of Hermite--Hadamard type for m-harmonic-arithmetically convex functions, ScienceAsia, 41: 5(2015), 357-361.