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    Fractional Hermite-Hadamard-type inequalities for interval-valued co-ordinated convex functions
    (De Gruyter Open Ltd, 2021) Budak, Hüseyin; Kara, H.; Ali, M. A.; Khan, S.; Chu, Y.
    In this work, we introduce the notions about the Riemann-Liouville fractional integrals for interval-valued functions on co-ordinates. We also establish Hermite-Hadamard and some related inequalities for co-ordinated convex interval-valued functions by applying the newly defined fractional integrals. The results of the present paper are the extension of several previously published results. © 2021 Huseyin Budak et al., published by De Gruyter.
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    NEW EXTENSIONS OF THE HERMITE-HADAMARD INEQUALITIES INVOLVING RIEMANN-LIOUVILLE FRACTIONAL INTEGRALS
    (Univ Miskolc Inst Math, 2020) Budak, Hüseyin; Kara, H.; Sarıkaya, Mehmet Zeki; Kiris, M. E.
    In this study, we establish the above and below bounds for the left and right hand sides of fractional Hermite-Hadamard inequalities by using functions whose second derivatives are bounded. We also give some refinements of fractional Hermite-Hadamard inequalities by using the functions that have the conditions f'(a + b - t) - f'(t) >= 0, t is an element of [a, a+b/2].
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    New Perspectives on Fractional Milne-Type Inequalities: Insights from Twice-Differentiable Functions
    (Emrah Evren KARA, 2024) Desta, H.D.; Budak, Hüseyin; Kara, H.
    This paper delves into an inquiry that centers on the exploration of fractional adaptations of Milne-type inequalities by employing the framework of twice-differentiable convex mappings. Leveraging the fundamental tenets of convexity, Hölder’s inequality, and the power-mean inequality, a series of novel inequalities are deduced. These newly acquired inequalities are fortified through insightful illustrative examples, bolstered by rigorous proofs. Furthermore, to lend visual validation, graphical representations are meticulously crafted for the showcased examples. © 2024, Emrah Evren KARA. All rights reserved.
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    On new versions of Hermite-Hadamard-type inequalities based on tempered fractional integrals
    (Univ Nis, Fac Sci Math, 2024) Budak, Hüseyin; Hezenci, F.; Tunc, T.; Kara, H.
    This research is on the new versions of Hermite-Hadamard type inequalities. These inequalities established by means of convex mappings include tempered fractional integral operators. Obtaining these inequalities, well-known Holder inequality and power mean inequality are also utilized. The resulting Hermite-Hadamard type inequalities are a generalization of some of the studies on this subject, including Riemann-Liouville fractional integrals. What's more, new results are obtained through special choices.