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    Quantum Hermite-Hadamard and quantum Ostrowski type inequalities for s-convex functions in the second sense with applications
    (Amer Inst Mathematical Sciences-Aims, 2021) Asawasamrit, Suphawat; Ali, Muhammad Aamir; Budak, Huseyin; Ntouyas, Sotiris K.; Tariboon, Jessada
    In this study, we use quantum calculus to prove Hermite-Hadamard and Ostrowski type inequalities for s-convex functions in the second sense. The newly proven results are also shown to be an extension of comparable results in the existing literature. Furthermore, it is provided that how the newly discovered inequalities can be applied to special means of real numbers.
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    Some New Simpson's-Formula-Type Inequalities for Twice-Differentiable Convex Functions via Generalized Fractional Operators
    (Mdpi, 2021) Ali, Muhammad Aamir; Kara, Hasan; Tariboon, Jessada; Asawasamrit, Suphawat; Budak, Hüseyin; Hezenci, Fatih
    From the past to the present, various works have been dedicated to Simpson's inequality for differentiable convex functions. Simpson-type inequalities for twice-differentiable functions have been the subject of some research. In this paper, we establish a new generalized fractional integral identity involving twice-differentiable functions, then we use this result to prove some new Simpson's-formula-type inequalities for twice-differentiable convex functions. Furthermore, we examine a few special cases of newly established inequalities and obtain several new and old Simpson's-formula-type inequalities. These types of analytic inequalities, as well as the methodologies for solving them, have applications in a wide range of fields where symmetry is crucial.