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    Extensions of Simpson's Inequality via Nonnegative Weight Functions and Fractional Operators
    (Wiley, 2025) Ogunmez, Hasan; Sarikaya, Mehmet Zeki
    In this paper, we present a new version of Simpson-type inequalities for differentiable functions defined on a subinterval of the positive real axis. The approach involves a nonnegative integrable weight function and provides an identity that refines the classical Simpson inequality by incorporating the first derivative of the function. A key aspect of this work is the inclusion of the Riemann-Liouville fractional integral, through which we derive specific inequalities that extend the classical framework. In certain cases, our results reduce to the well-known Simpson inequality, demonstrating the generality and flexibility of the method.MSC2020 Classification: 26A09, 26D10, 26D15, 33E20
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    On some Hermite-Hadamard type inequalities for strongly s-convex functions
    (Biska Bilişim, 2017) Erdem, Yusuf; Ogunmez, Hasan; Budak, Huseyin
    In this paper, we establish some new results related to the left-hand of theHermite-Hadamard type inequalities for the class of functions whose secondderivatives are strongly s-convex functions in the second sense. Someprevious results are also recaptured as a special case.
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    On the Fractional Inequalities of the Milne Type
    (Wiley, 2025) Budak, Hueseyin; Kara, Hasan; Ogunmez, Hasan
    Our investigations in this paper revolve around exploring fractional variants of inequalities of Milne type by applying twice differentiable convex mappings. Based on some principles of convexity, H & ouml;lder inequality, and power-mean inequality, novel inequalities are derived. The acquired inequalities are supported by illustrative examples, which are calculated via their proofs. Additionally, graphical representations are to verify the examples visually. Furthermore, this investigation unveils fresh findings within the realm of inequalities.
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    Some generalized inequalities of Hermite-Hadamard type for strongly s-convex functions
    (Biska Bilişim, 2017) Erdem, Yusuf; Ogunmez, Hasan; Budak, Huseyin
    In this paper, some new generalized results related to the left-hand and the right-hand of the Hermite-Hadamard inequalities for the class of functions whose derivatives are strongly-convex functions in the second sense are established. Some previous results are also recaptured as a special case.