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-Hermite–Hadamard Inequalities for Generalized Exponentially -Preinvex Functions
Journal of Mathematics ( IF 1.4 ) Pub Date : 2021-04-19 , DOI: 10.1155/2021/5577340
Hua Wang 1 , Humaira Kalsoom 2 , Hüseyin Budak 3 , Muhammad Idrees 4
Affiliation  

In this article, we introduce a new extension of classical convexity which is called generalized exponentially -preinvex functions. Also, it is seen that the new definition of generalized exponentially -preinvex functions describes different new classes as special cases. To prove our main results, we derive a new -integral identity for the twice -differentiable function. By using this identity, we show essential new results for Hermite–Hadamard-type inequalities for the -integral by utilizing differentiable exponentially -preinvex functions. The results presented in this article are unification and generalization of the comparable results in the literature.

中文翻译:

广义指数函数的-Hermite-Hadamard不等式-Preinvex函数

在本文中,我们介绍了经典凸性的新扩展,称为指数泛化 -预不变凸函数。此外,可以看出,广义的新定义是指数式的-预不变凸函数描述为特殊情况下,不同的新类。为了证明我们的主要结果,我们得出一个新的-对于两次积分身份-微函数。通过使用该恒等式,我们通过利用可微分的指数显示了-积分的Hermite–Hadamard型不等式的重要新结果-预不变凸函数。本文介绍的结果是文献中可比结果的统一和概括。
更新日期:2021-04-19
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