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    Fractional midpoint-type inequalities for twice-differentiable functions
    (Univ Nis, Fac Sci Math, 2023) Hezenci, Fatih; Bohner, Martin; Budaka, Huseyin
    In this research article, we obtain an identity for twice differentiable functions whose second derivatives in absolute value are convex. By using this identity, we prove several left Hermite-Hadamard-type inequalities for the case of Riemann-Liouville fractional integrals. Furthermore, we provide our results by using special cases of obtained theorems.
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    Post-quantum Hermite-Jensen-mercer inequalities
    (Rocky Mt Math Consortium, 2023) Bohner, Martin; Budak, Hüseyin; Kara, Hasan
    The Jensen-Mercer inequality, which is well known in the literature, has an important place in mathematics and related disciplines. In this work, we obtain the Hermite-Jensen-Mercer inequality for post-quantum integrals by utilizing Jensen-Mercer inequalities. Then we investigate the connections between our results and those in earlier works. Moreover, we give some examples to illustrate our main results. This is the first paper about Hermite-Jensen-Mercer inequalities for post-quantum integrals.