The Estimation of Different Kinds of Integral Inequalities for a Generalized Class of Convex Mapping and a Harmonic Set via Fuzzy Inclusion Relations and Their Applications in Quadrature Theory

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-05-22 DOI:10.3390/axioms13060344

A. Althobaiti, Saad Althobaiti, Miguel Vivas Cortez

引用次数: 0

Abstract

The relationship between convexity and symmetry is widely recognized. In fuzzy theory, both concepts exhibit similar behavior. It is crucial to remember that real and interval-valued mappings are special instances of fuzzy-number-valued mappings (F-N-V-Ms), as fuzzy theory relies on the unit interval, which is crucial to resolving problems with interval analysis and fuzzy number theory. In this paper, a new harmonic convexities class of fuzzy numbers has been introduced via up and down relation. We show several Hermite–Hadamard (H ⋅ H) and Fejér-type inequalities by the implementation of fuzzy Aumann integrals using the newly defined class of convexities. Some nontrivial examples are also presented to validate the main outcomes.

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通过模糊包容关系估算广义类凸映射和谐集的各类积分不等式及其在正交理论中的应用

凸性和对称性之间的关系已得到广泛认可。在模糊理论中，这两个概念表现出相似的行为。重要的是要记住实值映射和区间值映射是模糊数值映射（F-N-V-Ms）的特例，因为模糊理论依赖于单位区间，这对于解决区间分析和模糊数理论的问题至关重要。本文通过上下关系引入了一类新的模糊数谐波凸度。通过使用新定义的凸类实现模糊奥曼积分，我们展示了几个 Hermite-Hadamard (H ⋅ H) 和 Fejér 型不等式。为了验证主要成果，还提出了一些非难例。

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

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.