Yazar "You, Xue Xiao" seçeneğine göre listele

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    New Simpson type inequalities for twice differentiable functions via generalized fractional integrals
    (Amer Inst Mathematical Sciences-Aims, 2022) You, Xue Xiao; Hezenci, Fatih; Budak, Hüseyin; Kara, Hasan
    Fractional versions of Simpson inequalities for differentiable convex functions are extensively researched. However, Simpson type inequalities for twice differentiable functions are also investigated slightly. Hence, we establish a new identity for twice differentiable functions. Furthermore, by utilizing generalized fractional integrals, we prove several Simpson type inequalities for functions whose second derivatives in absolute value are convex.
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    Some Parameterized Quantum Simpson's and Quantum Newton's Integral Inequalities via Quantum Differentiable Convex Mappings
    (Hindawi Ltd, 2021) You, Xue Xiao; Ali, Muhammad Aamir; Budak, Hüseyin; Vivas-Cortez, Miguel J. J.; Qaisar, Shahid
    In this work, two generalized quantum integral identities are proved by using some parameters. By utilizing these equalities, we present several parameterized quantum inequalities for convex mappings. These quantum inequalities generalize many of the important inequalities that exist in the literature, such as quantum trapezoid inequalities, quantum Simpson's inequalities, and quantum Newton's inequalities. We also give some new midpoint-type inequalities as special cases. The results in this work naturally generalize the results for the Riemann integral.
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    Some parameterized Simpson's type inequalities for differentiable convex functions involving generalized fractional integrals
    (Springer, 2022) You, Xue Xiao; Ali, Muhammad Aamir; Budak, Hüseyin; Kara, Hasan; Zhao, Dafang
    In this paper, we establish some new inequalities of Simpson's type for differentiable convex functions involving some parameters and generalized fractional integrals. The results given in this study are a generalization of results proved in (Du, Li and Yang in Appl. Math. Comput. 293:358-369, 2017).