伪积分的Jensen不等式

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2021-06-01 DOI:10.22111/IJFS.2021.6084

Deli Zhang, E. Pap

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引用次数: 2

摘要

本文引入了一个基于半环$([a,b]，oplus, otimes)$的一般$(oplus,otimes)$-凸函数，它具有伪加法$oplus$和伪乘法$otimes。得到了有限ejensen不等式的推广，以及关于(0 +，times)凸函数的伪积分。这也推广了Lebesgue积分的Jensen不等式以及Pap和v{S}trboja引用{12}的结果。同时，我们还证明了半环$([a,b]， sup, otimes)$上关于非降函数的伪积分的Jensen不等式，并给出了广义模糊积分的相应结果。

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Jensen's inequalities for pseudo-integrals

In this paper, we introduce a general$(oplus,otimes)$-convex function based on semirings $([a,b],oplus, otimes)$ with pseudo-addition $oplus$ andpseudo-multiplication $otimes.$ The generalization of the finiteJensen's inequality, as well as pseudo-integral with respect to$(oplus,otimes)$-convex functions, is obtained. This also generalizes Jensen's inequalities for Lebesgue integral and the results of Pap and v{S}trboja cite{12}. Meanwhile, we also prove Jensen's inequalities for pseudo-integrals on semirings $([a,b], sup, otimes)$with respect to nondecreasing functions and present correspondingresults for generalized fuzzy integrals.

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.