Some New Inequalities of Hermite-Hadamard Type for Differentiable Godunova-Levin Functions via Fractional Integrals
Abstract
In this paper, we present new inequalities of the Hermite -– Hadamard type related to fractional integrals for Godunova-- Levin type functions. These inequalities are obtained with the help the of definitions of the Godunova-–Levin functions, the Holder and Power mean type inequalities.
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References
- [1] B. Martos, The Power of Nonlinear Programming Methods (In Hungarian). MTA Kozgazdas agtudom anyi Int ezet enek Kozlem enyei, No. 20, Budapest, Hungary, 1966.
- [2] M. Avriel, r–Convex Functions, Mathematical Programming, 2 (1972), 309-323.
- [3] S. S. Dragomir, C.E.M. Pearse, Selected Topics on Hermite–Hadamard Inequalities and Applications, RGMIA Monographs, Victoria University, 2000, [ONLINE. http://rgmia.org /papers/monographs/Master.pdf]
- [4] M. Z. Sarıkaya, A. Saglam and H. Yıldırım, On some Hadamard-type inequalities for hconvex functions, J. Math. Inequal. 2 (2008), 335–341.
- [5] L. Chun and F. Qi, Integral inequalities of Hermite–Hadamard type for functions whose third derivatives are convex. Journal of Inequalities and Applications. 2013:451.(2013)
- [6] S.. Wu, B. Sroysang, J.-S. Xie and Y.-M. Chu, Parametrized inequality of Hermite–Hadamard type for functions whose third derivative absolute values are quasi-convex, Wu et al. SpringerPlus. 4:831 (2015) Page 9 of 9.
- [7] I. Iscan, Hermite-Hadamard type inequalities for harmonically (alpha;m)convex functions, J. Hacettepe of Mathematics and Statistics 45 (2016) 2, 381–390. [8] J., Materano, N., Merentes and M., Valera–Lopez, On Inequalities Of Hermite–Hadamard Type for Stochastic Processes Whose Third Derivative Absolute Values Are Quasi–Convex, Tamkang Journal Of Mathematics. 48 (2017) 2, 203–208.
- [9] B. Bayraktar and M. Gurbuz, On some integral inequalities for (s;m)convex functions, TWMS J. App. Eng. Math., 10(2) (2020), 288–295.
Details
Primary Language
English
Subjects
Engineering
Journal Section
Conference Paper
Authors
Bahtiyar Bayraktar
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Türkiye
Publication Date
April 15, 2020
Submission Date
July 2, 2019
Acceptance Date
February 24, 2020
Published in Issue
Year 2020 Volume: 8 Number: 1
