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Some inequalities obtained by fractional integrals of positive real orders
Journal of Inequalities and Applications ( IF 1.6 ) Pub Date : 2020-06-03 , DOI: 10.1186/s13660-020-02418-5
Mustafa Gürbüz , Yakup Taşdan , Erhan Set

The primary objective of this study is to handle new generalized Hermite–Hadamard type inequalities with the help of the Katugampola fractional integral operator, which generalizes the Hadamard and Riemann–Liouville fractional integral operators into one system. In order to do this, a new fractional integral identity is obtained. Then, by using this identity, some inequalities for the class of functions whose derivatives in absolute values at certain powers are ρ-convex are derived. It is observed that the obtained inequalities are generalizations of some results in the literature.

中文翻译:

通过正实阶分数积分获得的一些不等式

这项研究的主要目的是借助Katugampola分式积分算子处理新的广义Hermite-Hadamard型不等式,该算子将Hadamard和Riemann-Liouville分式积分算子推广为一个系统。为此,获得了新的分数积分恒等式。然后,通过使用该恒等式,导出某些函数的不等式,这些函数的绝对值在某些幂处的导数为ρ-凸。可以看出,获得的不等式是文献中某些结果的概括。
更新日期:2020-06-03
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