Some new Hermite-Hadamard type inequalities for \(h\)-convex functions via quantum integral on finite intervals
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Authors
Limin Yang
- Basic Department, Henan Vocational College of Water Conservancy and Environment, Zhengzhou 450008, Henan, P. R. China
Ruiyun Yang
- Basic Department, Henan Vocational College of Water Conservancy and Environment, Zhengzhou 450008, Henan, P. R. China
Abstract
In this paper, we establish some new Hermite-Hadamard type inequalities for \(h\)-convex functions via quantum integral on finite intervals. The results presented here would provide extensions and corrections of those given in earlier works.
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ISRP Style
Limin Yang, Ruiyun Yang, Some new Hermite-Hadamard type inequalities for \(h\)-convex functions via quantum integral on finite intervals, Journal of Mathematics and Computer Science, 18 (2018), no. 1, 74--86
AMA Style
Yang Limin, Yang Ruiyun, Some new Hermite-Hadamard type inequalities for \(h\)-convex functions via quantum integral on finite intervals. J Math Comput SCI-JM. (2018); 18(1):74--86
Chicago/Turabian Style
Yang, Limin, Yang, Ruiyun. "Some new Hermite-Hadamard type inequalities for \(h\)-convex functions via quantum integral on finite intervals." Journal of Mathematics and Computer Science, 18, no. 1 (2018): 74--86
Keywords
- Hermite-Hadamard type inequalities
- \(h\)-convex functions
- integral inequalities
- quantum calculus
MSC
References
-
[1]
Y.-M. Bai, F. Qi, Some integral inequalities of the Hermite-Hadamard type for log-convex functions on co-ordinates, J. Nonlinear Sci. Appl., 9 (2016), 5900–5908
-
[2]
F. Chen, S. Wu, Several complementary inequalities to inequalities of Hermite-Hadamard type for s-convex functions, , J. Nonlinear Sci. Appl., 9 (2016), 705–716
-
[3]
F. Chen, W. Yang, Some new Chebyshev type quantum integral inequalities on finite intervals, J. Comput. Anal. Appl., 21 (2016), 417–426
-
[4]
L. Chun, F. Qi, Integral inequalities of Hermite-Hadamard type for functions whose third derivatives are convex, J. Inequal. Appl., 2013 (2013), 10 pages
-
[5]
S. S. Dragomir, Hermite-Hadamard’s type inequalities for operator convex functions, Appl. Math. Comput., 218 (2011), 766–772
-
[6]
S. S. Dragomir, M. I. Bhatti, M. Iqbal, M. Muddassar , Some new Hermite-Hadamard’s type fractional integral inequalities, J. Comput. Anal. Appl., 18 (2015), 655–661
-
[7]
S. S. Dragomir, C. E. M. Pearce, Selected Topics on Hermite-Hadamard Inequalities and Applications, RGMIA Monographs, Victoria University (2000)
-
[8]
L. Fejér, Über die Fourierreihen, II. , Math. Naturwiss. Anz Ungar. Akad. Wiss., 24 (1906), 369–390
-
[9]
I. İşcan, S. Wu, Hermite-Hadamard type inequalities for harmonically convex functions via fractional integrals, Appl. math. Comput., 238 (2014), 237–244
-
[10]
V. Kac, P. Cheung, Quantum Calculus, Springer, New York (2002)
-
[11]
W.-H. Li, F. Qi, Some Hermite-Hadamard type inequalities for functions whose n-th derivatives are (\(\alpha,m\))-convex, Filomat, 27 (2013), 1575–1582
-
[12]
Z. Liu, W. Yang, Some new Grüss type quantum integral inequalities on finite intervals, J. Nonlinear Sci. Appl., 9 (2016), 3362–3375
-
[13]
M. A. Noor, K. I. Noor, M. U. Awan, Some quantum estimates for Hermite-Hadamard inequalities, Appl. Math. Comput., 251 (2015), 675-679
-
[14]
J. E. Pečarić, F. Proschan, Y. L. Tong , Convex Functions, Partial Ordering and Statistical Applications, Academic Press, New York (1992)
-
[15]
M. Z. Sarikaya, A. Saglam, H. Yildirim, On some Hadamard-type inequalities for h-convex functions, J. Math. Inequal., 2 (2008), 335–341
-
[16]
W. Sudsutad, S. K. Ntouyas, J. Tariboon, Quantum integral inequalities for convex functions, J. Math. Inequal., 9 (2015), 781–793
-
[17]
J. Tariboon, S. K. Ntouyas, Quantum calculus on finite intervals and applications to impulsive difference equations, Adv. Differ. Equ., 2013 (2013 ), 19 pages
-
[18]
J. Tariboon, S. K. Ntouyas, Quantum integral inequalities on finite intervals, J. Inequal. Appl., 2014 (2014), 13 pages
-
[19]
M. Tunç, On new inequalities for h-convex functions via Riemann-Liouville fractional integration, Filomat, 27 (2013), 559–565
-
[20]
S. Varošanec , On h-convexity, J. Math. Anal. Appl., 326 (2007), 303–311
-
[21]
B. Xi, F. Qi, Y. Zhang, Some inequalities of Hermite-Hadamard type for m-harmonic-arithmetically convex functions, ScienceAsia, 41 (2015), 357–361
-
[22]
W. Yang, Hermite-Hadamard type inequalities for \((p_1, h_1)-(p_2, h_2)\)-convex functions on the co-ordinates, Tamkang J. Math., 47 (2016), 289–322
-
[23]
W. Yang, Some new Fejér type inequalities via quantum calculus on finite intervals, ScienceAsia, 43 (2017), 123–134