Hermite-Hadamard Type Inequalities For Two Times Differentiable Arithmetic-Harmonically Convex Functions
Abstract
In this work, by using both an
integral identity and the Hölder, the power-mean integral inequalities it is
established several new inequalities for two times differentiable
arithmetic-harmonically-convex function. Also, a few applications are given for
some means of real numbers.
Keywords
Convex function,arithmetic-harmonically-convex function,,Hermite-Hadamard’s inequality
References
- 1. S.S. Dragomir, Inequalities of Hermite-Hadamard type for AH-convex functions, Stud. Univ. Babeş-Bolyai Math. 61(4) (2016), 489-502.
- 2. S.S. Dragomir and C.E.M. Pearce, Selected Topics on Hermite-Hadamard Inequalities and Applications, RGMIA Monographs, Victoria University, 2000.
- 3. 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.
- 4. Sarikaya, M.Z. and Aktan, N., On the generalization of some integral inequalities and their applications, Mathematical and Computer Modelling, 54, (2011), 2175-2182.
- 5. 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.