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New Variant of Hermite–Jensen–Mercer Inequalities via Riemann–Liouville Fractional Integral Operators
Journal of Mathematics ( IF 1.4 ) Pub Date : 2020-08-01 , DOI: 10.1155/2020/4303727
Qiong Kang 1 , Saad Ihsan Butt 2 , Waqas Nazeer 3 , Mehroz Nadeem 2 , Jamshed Nasir 2 , Hong Yang 4
Affiliation  

In this paper, certain Hermite–Hadamard–Mercer-type inequalities are proved via Riemann–-Liouville fractional integral operators. We established several new variants of Hermite–Hadamard’s inequalities for Riemann–Liouville fractional integral operators by utilizing Jensen–Mercer inequality for differentiable mapping whose derivatives in the absolute values are convex. Moreover, we construct new lemmas for differentiable functions , , and and formulate related inequalities for these differentiable functions using variants of Hölder’s inequality.

中文翻译:

通过Riemann-Liouville分数阶积分算子得到Hermite-Jensen-Mercer不等式的新变体

在本文中,通过Riemann-Liouville分式积分算子证明了某些Hermite-Hadamard-Mercer型不等式。通过利用Jensen-Mercer不等式进行微分映射,其绝对值的导数是凸的,我们为Riemann-Liouville分式积分算子建立了Hermite-Hadamard不等式的几个新变式。此外,我们建设新的引理对微函数并制定相关的不平等使用赫尔德不等式的变体,这些微函数。
更新日期:2020-08-01
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