Inequalities of Hermite-Hadamard and Bullen Type for $AH$-Convex Functions
Inequalities of Hermite-Hadamard and Bullen Type for $AH$-Convex Functions
In this paper, by using an integral identity some new general inequalities of the Hermite-Hadamard and Bullen type for functions whose second derivatives in absolute value at certain power are arithmetically-harmonically convex are obtained. Some applications to special means of real numbers are also given.
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- [1] K. Bekar, Inequalities for three-times differentiable arithmetic-harmonically functions, Turkish J. Anal. Number Theory, (Accepted for publication),
(2019).
- [2] S.S. Dragomir, Inequalities of Hermite-Hadamard type for AH-convex functions, Stud. Univ. Babes¸-Bolyai Math. 61(4) (2016), 489-502.
- [3] S.S. Dragomir and C.E.M. Pearce, Selected Topics on Hermite-Hadamard Inequalities and Applications, RGMIA Monographs, Victoria University,
(2000).
- [4] İ. İşcan, T. Toplu and F. Yetgin, Some new inequalities on generalization of Hermite-Hadamard and Bullen type inequalities, Kragujevac J. Math.,
(Accepted for publication), 2019.
- [5] H. Kadakal, Some New Integral Inequalities for n-Times Differentiable Strongly r-Convex Functions, J. Funct. Spaces, Volume 2019, Article ID 1219237,
10 pages, (2019).
- [6] H. Kadakal, Hermite-Hadamard type inequalities for two times differentiable arithmetic-harmonically convex functions, Cumhuriyet Sci. J., (Accepted
for publication), (2019).
- [7] M. Kadakal and İ. İşcan, Some new inequalities for differentiable arithmetic-harmonically convex functions, C. R. Acad. Bulgare Sci, (Submitted to
journal), (2019).
- [8] S. Maden, H. Kadakal, M. Kadakal and İ. İşcan, Some new integral inequalities for n-times differentiable convex and concave functions. J. Nonlinear
Sci. Appl., 10 (2017), 6141–6148.
- [9] M. Z. Sarikaya and N. Aktan, On the generalization of some integral inequalities and their applications, Math. Comput. Model. Dyn. Syst., 54, (2011),
2175-2182.
- [10] T. Y. Zhang and F. Qi, Integral Inequalities of Hermite–Hadamard Type for m-AH Convex Functions, Turkish J. Anal. Number Theory, 2(3) (2014),
60-64.