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Mathematics 2019, 7(2), 183; https://doi.org/10.3390/math7020183

New Integral Inequalities via the Katugampola Fractional Integrals for Functions Whose Second Derivatives Are Strongly η-Convex

1
Department of Mathematics and Computer Science, Alabama State University, Montgomery, AL 36101, USA
2
Department of Mathematics, Tuskegee University, Tuskegee, AL 36088, USA
*
Author to whom correspondence should be addressed.
Received: 28 December 2018 / Revised: 3 February 2019 / Accepted: 12 February 2019 / Published: 15 February 2019
(This article belongs to the Special Issue Inequalities)
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Abstract

In this paper, we introduced some new integral inequalities of the Hermite–Hadamard type for functions whose second derivatives in absolute values at certain powers are strongly η -convex functions via the Katugampola fractional integrals. View Full-Text
Keywords: Hermite–Hadamard type inequality; strongly η-convex functions; Hölder’s inequality; Power mean inequality; Katugampola fractional integrals; Riemann–Liouville fractional integrals; Hadamard fractional integrals Hermite–Hadamard type inequality; strongly η-convex functions; Hölder’s inequality; Power mean inequality; Katugampola fractional integrals; Riemann–Liouville fractional integrals; Hadamard fractional integrals
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).
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Kermausuor, S.; Nwaeze, E.R.; Tameru, A.M. New Integral Inequalities via the Katugampola Fractional Integrals for Functions Whose Second Derivatives Are Strongly η-Convex. Mathematics 2019, 7, 183.

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