{"title":"类sec算法的收敛性及其在广义分数阶微积分中的应用","authors":"G. Anastassiou, I. Argyros","doi":"10.4064/AM2275-12-2015","DOIUrl":null,"url":null,"abstract":"We present local and semilocal convergence results for secantlike algorithms in order to approximate a locally unique solution of a nonlinear equation in a Banach space setting. In the last part of the study we present some choices of the operators involved in fractional calculus where the operators satisfy the convergence conditions.","PeriodicalId":52313,"journal":{"name":"Applicationes Mathematicae","volume":"30 1","pages":"191-206"},"PeriodicalIF":0.0000,"publicationDate":"2016-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":"{\"title\":\"On the convergence of secant-like algorithms with applications to generalized fractional calculus\",\"authors\":\"G. Anastassiou, I. Argyros\",\"doi\":\"10.4064/AM2275-12-2015\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We present local and semilocal convergence results for secantlike algorithms in order to approximate a locally unique solution of a nonlinear equation in a Banach space setting. In the last part of the study we present some choices of the operators involved in fractional calculus where the operators satisfy the convergence conditions.\",\"PeriodicalId\":52313,\"journal\":{\"name\":\"Applicationes Mathematicae\",\"volume\":\"30 1\",\"pages\":\"191-206\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2016-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"2\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Applicationes Mathematicae\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.4064/AM2275-12-2015\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"Mathematics\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Applicationes Mathematicae","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.4064/AM2275-12-2015","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"Mathematics","Score":null,"Total":0}
On the convergence of secant-like algorithms with applications to generalized fractional calculus
We present local and semilocal convergence results for secantlike algorithms in order to approximate a locally unique solution of a nonlinear equation in a Banach space setting. In the last part of the study we present some choices of the operators involved in fractional calculus where the operators satisfy the convergence conditions.
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