Inequalities of Hermite-Hadamard and Bullen Type for Three Times Differentiable $AH$-Convex Functions

Year 2019, Volume: 7 Issue: 2, 442 - 448, 15.10.2019

Huriye Kadakal , Kerim Bekar

https://izlik.org/JA23XM49KP

Abstract

In this paper, after introducing a new integral identity, by using this integral identity we obtain some new general inequalities of the Hermite-Hadamard and Bullen type for functions whose third derivatives in absolute value at certain power are arithmetically-harmonically convex. Some applications to special means of real numbers are also given.

Keywords

Convex function , AH-convex function , Hermite-Hadamard and Bullen type inequality

References

• [1] K. Bekar, Inequalities for three-times differentiable arithmetic-harmonically functions, Turkish Journal of Analysis and 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 Journal of Mathematics, (Accepted for publication), (2019).
• [5] H. Kadakal, New Inequalities for Strongly r-Convex Functions, Journal of Function 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., Vol.40-3 (2019) 670-678.
• [7] M. Kadakal and İ. İşcan, Some new inequalities for differentiable arithmetic-harmonically convex functions, Comptes Rendus De L’Academie Bulgare Des Sciences, (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, Mathematical and Computer Modelling, 54, (2011), 2175-2182.
• [10] F. Yetgin, M. Korkmaz and İ. İşcan, Some new type general integral inequalities for s-convex functions and related results, January (2017), doi: 10.13140/RG.2.2.22315.64805.
• [11] T.Y. Zhang and F. Qi, Integral Inequalities of Hermite–Hadamard Type for m-AH Convex Functions, Turkish Journal of Analysis and Number Theory, 2(3) (2014), 60-64.