{"title":"Representations for Maximal Monotone Operators of Type (D) in Banach Spaces","authors":"Bao T. Nguyen, Tran N. Nguyen, Huynh M. Hien","doi":"10.1007/s10957-024-02457-8","DOIUrl":null,"url":null,"abstract":"<p>The present paper deals with a maximal monotone operator <i>A</i> of type (D) in a Banach space whose dual space is strictly convex. We establish some representations for the value <i>Ax</i> at a given point <i>x</i> via its values at nearby points of <i>x</i>. We show that the faces of <i>Ax</i> are contained in the set of all weak<span>\\(^*\\)</span> convergent limits of bounded nets of the operator at nearby points of <i>x</i>, then we obtain a representation for <i>Ax</i> by use of this set. In addition, representations for the support function of <i>Ax</i> based on the minimal-norm selection of the operator in certain Banach spaces are given.</p>","PeriodicalId":1,"journal":{"name":"Accounts of Chemical Research","volume":null,"pages":null},"PeriodicalIF":16.4000,"publicationDate":"2024-06-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Accounts of Chemical Research","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s10957-024-02457-8","RegionNum":1,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"CHEMISTRY, MULTIDISCIPLINARY","Score":null,"Total":0}
引用次数: 0
Abstract
The present paper deals with a maximal monotone operator A of type (D) in a Banach space whose dual space is strictly convex. We establish some representations for the value Ax at a given point x via its values at nearby points of x. We show that the faces of Ax are contained in the set of all weak\(^*\) convergent limits of bounded nets of the operator at nearby points of x, then we obtain a representation for Ax by use of this set. In addition, representations for the support function of Ax based on the minimal-norm selection of the operator in certain Banach spaces are given.
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.
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