通过加权蒙哥马利特性的扩展实现 n 凸函数的波波维奇丘型不等式

Studia Universitatis Babes-Bolyai Matematica Pub Date : 2024-03-15 DOI:10.24193/subbmath.2024.1.02

Asif R. Khan, Hira Nabi, J. Pečarić

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摘要

在本文中，我们利用蒙哥马利特性和格林函数扩展的加权版本，推导出波波维奇型不等式。同时还得到了一些关于某点上 n 个凸函数的结果。此外，还提出了一些奥斯特洛夫斯基式不等式，这些不等式与所得到的不等式相互关联：26A51, 26D15, 26D20.2021 年 9 月 26 日收到；2022 年 5 月 13 日接受

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Popoviciu type inequalities for n-convex functions via extension of weighted Montgomery identity

In this article, we derive the Popoviciu-type inequalities by using the weighted version of the extension of Montgomery’s identity and Green functions. Some results for n-convex functions at a point are also obtained. Besides that, some Ostrowski-type inequalities are also presented, which are interrelated with the obtained inequalities. Mathematics Subject Classification (2010): 26A51, 26D15, 26D20. Received 26 September 2021; Accepted 13 May 2022

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Studia Universitatis Babes-Bolyai Matematica

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