Some new Inequalities for Differentiable Arithmetic-Harmonically Convex Functions
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Authors: M. KADAKAL, P. AGARWAL AND I. .{I}C{S}CAN
DOI: 10.46793/KgJMat2505.669K
Abstract:
In this study, by using an integral identity together with both the Hölder and the power-mean inequalities for integrals we establish several new inequalities for differentiable arithmetic-harmonically-convex function. Also, we give some applications for special means.
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. https://ssrn.com/abstract=
3158351
[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. https:
//doi:10.22436/jnsa.010.12.01
[4] M. Z. Sarikaya and N. Aktan, On the generalization of some integral inequalities and their
applications, Math. Comput. Modelling 54 (2011), 2175–2182. https://doi.org/10.1016/j.
mcm.2011.05.026
[5] T. Y. Zhang and F. Qi, Integral Inequalities of Hermite-Hadamard type for m-AH con-
vex functions, Turkish Journal of Analysis and Number Theory 2(3) (2014), 60-64. https:
//doi.org/10.12691/tjant-2-3-1