{"title":"Newton's method for generalized equations under weak conditions","authors":"I. Argyros, S. George","doi":"10.55630/serdica.2023.49.269-282","DOIUrl":null,"url":null,"abstract":"A local convergence analysis is developed for Newton’s method in order to approximate a solution of a generalized equations in a Banach space setting. The convergence conditions are based on generalized continuity conditions on the Fr´echet derivative of the operator involved and the Aubin property. The specialized cases of our results extend earlier ones using similar information.","PeriodicalId":509503,"journal":{"name":"Serdica Mathematical Journal","volume":"29 7","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-01-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Serdica Mathematical Journal","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.55630/serdica.2023.49.269-282","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
A local convergence analysis is developed for Newton’s method in order to approximate a solution of a generalized equations in a Banach space setting. The convergence conditions are based on generalized continuity conditions on the Fr´echet derivative of the operator involved and the Aubin property. The specialized cases of our results extend earlier ones using similar information.
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