{"title":"一类迭代函数方程的平稳解","authors":"Weiwei Shi, Xiao Tang","doi":"10.1007/s00010-024-01085-x","DOIUrl":null,"url":null,"abstract":"<div><p>Imposing some conditions on derivatives of the known functions, using the Fiber Contraction Theorem we prove the existence of <span>\\(C^1\\)</span> solutions of a class of iterative functional equations which involves iterates of the unknown functions and a nonlinear term.</p></div>","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-05-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Smooth solutions of a class of iterative functional equations\",\"authors\":\"Weiwei Shi, Xiao Tang\",\"doi\":\"10.1007/s00010-024-01085-x\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>Imposing some conditions on derivatives of the known functions, using the Fiber Contraction Theorem we prove the existence of <span>\\\\(C^1\\\\)</span> solutions of a class of iterative functional equations which involves iterates of the unknown functions and a nonlinear term.</p></div>\",\"PeriodicalId\":0,\"journal\":{\"name\":\"\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0,\"publicationDate\":\"2024-05-27\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s00010-024-01085-x\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s00010-024-01085-x","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Smooth solutions of a class of iterative functional equations
Imposing some conditions on derivatives of the known functions, using the Fiber Contraction Theorem we prove the existence of \(C^1\) solutions of a class of iterative functional equations which involves iterates of the unknown functions and a nonlinear term.
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