指数凸函数的Simpson型不等式及其应用

Yenny Rangel-Oliveros, E. Nwaeze
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引用次数: 2

摘要

Simpson不等式不能应用于两次可微但不是四次可微的函数,或者在所考虑的区间中具有有界四阶导数的函数。许多文章都是关于两次可微凸函数的,但据我们所知,对于两次可微分指数凸函数和拟凸函数,还没有什么是已知的。在本文中,我们的目的是公正地对待这一质疑。为此,我们证明了指数凸函数和指数拟凸函数的几个Simpson型不等式。我们的发现完善、概括和补充了文献中现有的结果。我们通过服用\(\alpha=0\)重新获得以前已知的结果。此外,我们还通过将结果应用于正实数的一些特殊均值和Simpson求积规则来表明我们的结果的重要性。所得结果可以推广到不同类型的凸函数。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Simpson’s type inequalities for exponentially convex functions with applications
The Simpson's inequality cannot be applied to a function that is twice differentiable but not four times differentiable or have a bounded fourth derivative in the interval under consideration. Loads of articles are bound for twice differentiable convex functions but nothing, to the best of our knowledge, is known yet for twice differentiable exponentially convex and quasi-convex functions. In this paper, we aim to do justice to this query. For this, we prove several Simpson's type inequalities for exponentially convex and exponentially quasi-convex functions. Our findings refine, generalize and complement existing results in the literature. We regain previously known results by taking \(\alpha=0\). In addition, we also show the importance of our results by applying them to some special means of positive real numbers and to Simpson's quadrature rule. The obtained results can be extended for different kinds of convex functions.
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