Browsing by Author "Korus, Peter"

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    Some new jensen-mercer type integral inequalities via fractional operators
    (Mdpi, 2023-06-01) Korus, Peter; Valdes, Juan Eduardo Napoles; Bayraktar, Bahtiyar; BAYRAKTAR, BAHTİYAR; Bursa Uludağ Üniversitesi/Eğitim Fakültesi.; 0000-0001-7594-8291; ABI-7823-2020
    In this study, we present new variants of the Hermite-Hadamard inequality via non-conformable fractional integrals. These inequalities are proven for convex functions and differentiable functions whose derivatives in absolute value are generally convex. Our main results are established using the classical Jensen-Mercer inequality and its variants for (h,m)-convex modified functions proven in this paper. In addition to showing that our results support previously known results from the literature, we provide examples of their application.
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    Weighted hermite-hadamard integral inequalities for general convex functions
    (Amer Inst Mathematical Sciences-aims, 2023-01-01) Korus, Peter; Valdes, Juan Eduardo Napoles; Bayraktar, Bahtiyar; BAYRAKTAR, BAHTİYAR; Bursa Uludağ Üniversitesi/Eğitim Fakültesi.; 0000-0001-7594-8291; ABI-7823-2020
    In this article, starting with an equation for weighted integrals, we obtained several extensions of the well-known Hermite-Hadamard inequality. We used generalized weighted integral operators, which contain the Riemann-Liouville and the k-Riemann-Liouville fractional integral operators. The functions for which the operators were considered satisfy various conditions such as the h-convexity, modified h-convexity and s-convexity.