Relatively Monotone and Relatively Generalized Monotone Maps in Nonsmooth Setting and Relative r-Monotonicity

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2023-01-20 DOI:10.1080/01630563.2022.2119248

Youness Alhabib Fajri

引用次数: 0

Abstract

Abstract The aim of this article is twofold. First, we consider relatively monotone, relatively pseudomonotone, and relatively quasimonotone maps in nonsmooth setting. For continuous maps, we describe -monotonicity when the relative parameters are different and prove that -quasimonotonicity implies -quasimonotonicity as well as -pseudomonotonicity implies -pseudomonotonicity. Then, under local Lipschitzianity assumption, we establish first-order criteria for -monotonicity, -pseudomonotonicity, and -quasimonotonicity. Second, we introduce and study the new notion of relatively r-monotone operators. We provide characterizations and properties. We give in particular criteria of first order for relative r-monotonicity, in smooth and nonsmooth locally Lipschitz settings, when the relative parameters are equal.

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非光滑环境下的相对单调和相对广义单调映射及相对r-单调性

摘要这篇文章的目的是双重的。首先，我们考虑非光滑环境中的相对单调、相对伪单调和相对拟单调映射。对于连续映射，当相对参数不同时，我们描述了-单调性，并证明了-拟单调性意味着-拟单调，以及-伪单调性暗示着-伪单调。然后，在局部Lipschitzianity假设下，我们建立了-单调性、-伪单调性和-拟单调性的一阶准则。其次，我们引入并研究了相对r单调算子的新概念。我们提供了特性和性质。在光滑和非光滑局部Lipschitz设置中，当相对参数相等时，我们给出了相对r单调性的一阶特殊准则。

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.