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October 2019 Some new refinement of Hermite-Hadamard type inequalities and their applications
Artion Kashuri, Rozana Liko, Silvestru Sever Dragomir
Tbilisi Math. J. 12(4): 159-188 (October 2019). DOI: 10.32513/tbilisi/1578020575

Abstract

In this paper first, we prove some new refinement of Hermite-Hadamard type inequalities for the convex function $f$. Second, by using five new integral identities, we present some new Riemann-Liouville fractional trapezoid and midpoint type inequalities. Third, using these results, we present applications to $f$-divergence measures. At the end, some new bounds for special means of different positive real numbers and new error estimates for the trapezoidal and midpoint formula are provided as well. These results give us the generalizations and improvements of the earlier results.

Citation

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Artion Kashuri. Rozana Liko. Silvestru Sever Dragomir. "Some new refinement of Hermite-Hadamard type inequalities and their applications." Tbilisi Math. J. 12 (4) 159 - 188, October 2019. https://doi.org/10.32513/tbilisi/1578020575

Information

Received: 8 April 2019; Accepted: 10 November 2019; Published: October 2019
First available in Project Euclid: 3 January 2020

zbMATH: 07179179
MathSciNet: MR4047583
Digital Object Identifier: 10.32513/tbilisi/1578020575

Subjects:
Primary: 26A51‎
Secondary: 26A33, 26D07, 26D10, 26D15

Rights: Copyright © 2019 Tbilisi Centre for Mathematical Sciences

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Vol.12 • No. 4 • October 2019
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