关于正、递减和凸的函数和逆：以及Stieltjes函数

IF 0.1 Q4 MATHEMATICS Cogent mathematics & statistics Pub Date : 2018-01-01 DOI:10.1080/25742558.2018.1477543

Grant Keady, N. Khajohnsaksumeth, N. Khajohnsaksumeth, B. Wiwatanapataphee

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引用次数: 2

摘要

任何从其上递减且凸的函数都有一个正的、递减的、凸的逆。当具有某种形式的广义凸性时，我们确定继承的额外凸性性质。当它是正的、递减的和凸的时，它的逆是凸的。开发了与Stieltjes函数何时相关的相关性质。通过超越方程用Stieltjes函数说明了结果。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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On functions and inverses, both positive, decreasing and convex: And Stieltjes functions

Abstract Any function from onto which is decreasing and convex has an inverse which is positive, decreasing and convex. When has some form of generalized convexity we determine additional convexity properties inherited by . When is positive, decreasing and -convex, its inverse is -convex. Related properties which pertain when is a Stieltjes function are developed. The results are illustrated with the Stieltjes function via a transcendental equation.

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