Hermite-Hadamard and Hermite-Hadamard-Fejér type Inequalities for Generalized Fractional Integrals

Abstract

In this paper we obtain the Hermite-Hadamard and Hermite-Hadamard-Fejér type inequalities for fractional integrals which generalize the two familiar fractional integrals namely, the Riemann-Liouville and the Hadamard fractional integrals into a single form. We prove that, in most cases, we obtain the Riemann--Liouville and the Hadamard equivalence just by taking limits when a parameter $\rho \to 1$ and $\rho \to 0^{+}$, respectively.

arXiv commentAccepted Manuscript. 14 pages, Journal of Mathematical Analysis and Applications (2016)

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• A Systematic Review on Hermite-Hadamard Inequality: Theory and Applications
• Hermite-Hadamard inequalities for (p,a,b)-convex functions