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Generalized Fejér–Hermite–Hadamard type via generalized (h−m)-convexity on fractal sets and applications
Chaos, Solitons & Fractals ( IF 5.3 ) Pub Date : 2021-04-16 , DOI: 10.1016/j.chaos.2021.110938
Ohud Almutairi , Adem Kiliçman

In this article, we define a new class of convexity called generalized (hm)-convexity, which generalizes h-convexity and m-convexity on fractal set Rα (0<α1). Some properties of this new class are discussed. Using local fractional integrals and generalized (hm)-convexity, we generalized Hermite–Hadamard (H–H) and Fejér–Hermite–Hadamard (Fejér–H–H) types inequalities. We also obtained a new result of the Fejér–H–H type for the function whose derivative in absolute value is the generalized (hm)-convexity on fractal sets. As applications, we studied some new inequalities for random variables, numerical integrations and generalized to special means.



中文翻译:

广义Fejér–Hermite–Hadamard类型 H-分形集的凸性及其应用

在本文中,我们定义了一类新的凸性,称为广义 H--凸性,泛化 H-凸性和 分形集上的凸性 [Rα 0<α1个。讨论了这个新类的一些属性。使用局部分数积分和广义H--凸性,我们推广了Hermite–Hadamard(H–H)和Fejér–Hermite–Hadamard(Fejér–H–H)类型的不等式。我们还获得了Fejér–H–H型函数的新结果,该函数的绝对值导数是广义的H-分形集的凸性。作为应用,我们研究了随机变量,数值积分的新不等式,并推广到了特殊的均值。

更新日期:2021-04-16
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