We provide a unified approach to getting Hermite–Hadamard inequalities for functions with convex absolute values of the second derivatives via the Riemann–Liouville integrals. Some particular inequalities generalizing the classical results, such as the trapezoid inequality, Simpson’s inequality, and midpoint inequality are also presented.
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Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 70, No. 12, pp. 1696–1706, December, 2018.
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Chen, F.X. On the Generalization of Some Hermite–Hadamard Inequalities for Functions with Convex Absolute Values of the Second Derivatives Via Fractional Integrals. Ukr Math J 70, 1953–1965 (2019). https://doi.org/10.1007/s11253-019-01618-7
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DOI: https://doi.org/10.1007/s11253-019-01618-7