广义分数积分Hermite-Hadamard不等式的新扩展

Q4 Mathematics

Communications in Mathematical Analysis Pub Date : 2020-12-06 DOI:10.22130/SCMA.2020.121963.759

H. Budak, Ebru Pehlivan, Pınar Kosem

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引用次数: 11

摘要

本文利用二阶导数有界的函数，建立了广义分数积分的一些梯形和中点型不等式。作为主要结果的特例，我们还给出了$k$-Riemann-Liouville分数积分的一些新不等式。利用条件$f^{prime}（a+b-x）geqf^{preme}（x）$，我们还得到了一些Hermite-Hadamard型不等式{2}right]$而不是凸性。

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On New Extensions of Hermite-Hadamard Inequalities for Generalized Fractional Integrals

In this paper, we establish some Trapezoid and Midpoint type inequalities for generalized fractional integrals by utilizing the functions whose second derivatives are bounded . We also give some new inequalities for $k$-Riemann-Liouville fractional integrals as special cases of our main results. We also obtain some Hermite-Hadamard type inequalities by using the condition $f^{prime }(a+b-x)geq f^{prime }(x)$ for all $xin left[ a,frac{a+b}{2}right] $ instead of convexity.

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Communications in Mathematical Analysis Mathematics-Applied Mathematics

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