{"title":"石川迭代法之外的迭代方案生成法","authors":"Atsumasa Kondo","doi":"10.1007/s00208-024-02977-8","DOIUrl":null,"url":null,"abstract":"<p>We propose an iterative scheme generating method to address common fixed point problems. Our approach yields diverse iterative schemes for finding common fixed points. The derivative results include the Ishikawa iterative method and its variations. An application to the variational inequality problem is provided to illustrate the usefulness of our method. The class of mappings we target is general. This category includes nonexpansive mappings and various other types, even those that lack continuity.</p>","PeriodicalId":18304,"journal":{"name":"Mathematische Annalen","volume":"31 1","pages":""},"PeriodicalIF":1.3000,"publicationDate":"2024-08-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Iterative scheme generating method beyond Ishikawa iterative method\",\"authors\":\"Atsumasa Kondo\",\"doi\":\"10.1007/s00208-024-02977-8\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>We propose an iterative scheme generating method to address common fixed point problems. Our approach yields diverse iterative schemes for finding common fixed points. The derivative results include the Ishikawa iterative method and its variations. An application to the variational inequality problem is provided to illustrate the usefulness of our method. The class of mappings we target is general. This category includes nonexpansive mappings and various other types, even those that lack continuity.</p>\",\"PeriodicalId\":18304,\"journal\":{\"name\":\"Mathematische Annalen\",\"volume\":\"31 1\",\"pages\":\"\"},\"PeriodicalIF\":1.3000,\"publicationDate\":\"2024-08-23\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Mathematische Annalen\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1007/s00208-024-02977-8\",\"RegionNum\":2,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematische Annalen","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s00208-024-02977-8","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
We propose an iterative scheme generating method to address common fixed point problems. Our approach yields diverse iterative schemes for finding common fixed points. The derivative results include the Ishikawa iterative method and its variations. An application to the variational inequality problem is provided to illustrate the usefulness of our method. The class of mappings we target is general. This category includes nonexpansive mappings and various other types, even those that lack continuity.
期刊介绍：
Begründet 1868 durch Alfred Clebsch und Carl Neumann. Fortgeführt durch Felix Klein, David Hilbert, Otto Blumenthal, Erich Hecke, Heinrich Behnke, Hans Grauert, Heinz Bauer, Herbert Amann, Jean-Pierre Bourguignon, Wolfgang Lück und Nigel Hitchin.
The journal Mathematische Annalen was founded in 1868 by Alfred Clebsch and Carl Neumann. It was continued by Felix Klein, David Hilbert, Otto Blumenthal, Erich Hecke, Heinrich Behnke, Hans Grauert, Heinz Bauer, Herbert Amann, Jean-Pierre Bourguigon, Wolfgang Lück and Nigel Hitchin.
Since 1868 the name Mathematische Annalen stands for a long tradition and high quality in the publication of mathematical research articles. Mathematische Annalen is designed not as a specialized journal but covers a wide spectrum of modern mathematics.
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