{"title":"林氏引理的推广","authors":"M. Mansour, M. Bahraoui, A. E. Bekkali","doi":"10.22436/jnsa.014.01.06","DOIUrl":null,"url":null,"abstract":"It follows from [A. L. Dontchev, R. T. Rockafellar, Springer, New York, (2014), Theorem 5I.3] that the distance from a point x to the set of fixed points of a set-valued contraction mapping Φ is bounded by a constant times the distance from x to Φ(x). In this paper, we generalize both this result and Lim’s lemma for a larger class of set-valued mappings instead of the class of set-valued contraction mappings. As consequence, we obtain some known fixed points theorems.","PeriodicalId":22770,"journal":{"name":"The Journal of Nonlinear Sciences and Applications","volume":"1 1","pages":"48-53"},"PeriodicalIF":0.0000,"publicationDate":"2020-06-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"A generalization of Lim's lemma\",\"authors\":\"M. Mansour, M. Bahraoui, A. E. Bekkali\",\"doi\":\"10.22436/jnsa.014.01.06\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"It follows from [A. L. Dontchev, R. T. Rockafellar, Springer, New York, (2014), Theorem 5I.3] that the distance from a point x to the set of fixed points of a set-valued contraction mapping Φ is bounded by a constant times the distance from x to Φ(x). In this paper, we generalize both this result and Lim’s lemma for a larger class of set-valued mappings instead of the class of set-valued contraction mappings. As consequence, we obtain some known fixed points theorems.\",\"PeriodicalId\":22770,\"journal\":{\"name\":\"The Journal of Nonlinear Sciences and Applications\",\"volume\":\"1 1\",\"pages\":\"48-53\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2020-06-13\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"The Journal of Nonlinear Sciences and Applications\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.22436/jnsa.014.01.06\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"The Journal of Nonlinear Sciences and Applications","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.22436/jnsa.014.01.06","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
摘要
它由[A]L. Dontchev, R. T. Rockafellar, Springer, New York， (2014)， Theorem 5I。3]点x到集值收缩映射Φ的不动点集的距离以一个常数乘以x到Φ(x)的距离为界。在本文中，我们将这一结果和Lim引理推广到一个更大的集值映射类，而不是集值收缩映射类。由此，我们得到了一些已知的不动点定理。
It follows from [A. L. Dontchev, R. T. Rockafellar, Springer, New York, (2014), Theorem 5I.3] that the distance from a point x to the set of fixed points of a set-valued contraction mapping Φ is bounded by a constant times the distance from x to Φ(x). In this paper, we generalize both this result and Lim’s lemma for a larger class of set-valued mappings instead of the class of set-valued contraction mappings. As consequence, we obtain some known fixed points theorems.
求助内容：
应助结果提醒方式：
京公网安备 11010802042870号
