Jensen's inequalities for pseudo-integrals

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

引用次数: 2

Abstract

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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伪积分的Jensen不等式

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。

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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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

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