某些Banach空间中Hammerstein包含的算法

Journal of Nonlinear Sciences and Applications Pub Date : 2019-02-04 DOI:10.22436/JNSA.012.06.05

M. Sene, M. Ndiaye, N. Djitté

{"title":"某些Banach空间中Hammerstein包含的算法","authors":"M. Sene, M. Ndiaye, N. Djitté","doi":"10.22436/JNSA.012.06.05","DOIUrl":null,"url":null,"abstract":"Let E be a reflexive smooth and strictly convex real Banach space. Let F : E → 2E and K : E∗ → E be bounded maximal monotone mappings such that D(F) = E and R(F) = D(K) = E∗. Suppose that the Hammerstein inclusion 0 ∈ u+ KFu has a solution in E. We present in this paper a new algorithm for approximating solutions of the inclusion 0 ∈ u+ KFu. Then we prove strong convergence theorems. Our theorems improve and unify most of the results that have been proved in this direction for this important class of nonlinear mappings. Furthermore, our technique of proof is of independent interest.","PeriodicalId":48799,"journal":{"name":"Journal of Nonlinear Sciences and Applications","volume":"205 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2019-02-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Algorithms for Hammerstein inclusions in certain Banach spaces\",\"authors\":\"M. Sene, M. Ndiaye, N. Djitté\",\"doi\":\"10.22436/JNSA.012.06.05\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Let E be a reflexive smooth and strictly convex real Banach space. Let F : E → 2E and K : E∗ → E be bounded maximal monotone mappings such that D(F) = E and R(F) = D(K) = E∗. Suppose that the Hammerstein inclusion 0 ∈ u+ KFu has a solution in E. We present in this paper a new algorithm for approximating solutions of the inclusion 0 ∈ u+ KFu. Then we prove strong convergence theorems. Our theorems improve and unify most of the results that have been proved in this direction for this important class of nonlinear mappings. Furthermore, our technique of proof is of independent interest.\",\"PeriodicalId\":48799,\"journal\":{\"name\":\"Journal of Nonlinear Sciences and Applications\",\"volume\":\"205 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2019-02-04\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Nonlinear Sciences and Applications\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.22436/JNSA.012.06.05\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Nonlinear Sciences and Applications","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.22436/JNSA.012.06.05","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

设E是一个自反光滑严格凸实巴拿赫空间。设F: E→2E和K: E∗→E是有界极大单调映射，使得D(F) = E和R(F) = D(K) = E∗。假设Hammerstein包含0∈u+ KFu在e中有解，本文给出了一个新的算法来逼近包含0∈u+ KFu的解。然后证明强收敛定理。对于这类重要的非线性映射，我们的定理改进并统一了在这个方向上已经证明的大多数结果。此外，我们的证明技术是独立的兴趣。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

Algorithms for Hammerstein inclusions in certain Banach spaces

Let E be a reflexive smooth and strictly convex real Banach space. Let F : E → 2E and K : E∗ → E be bounded maximal monotone mappings such that D(F) = E and R(F) = D(K) = E∗. Suppose that the Hammerstein inclusion 0 ∈ u+ KFu has a solution in E. We present in this paper a new algorithm for approximating solutions of the inclusion 0 ∈ u+ KFu. Then we prove strong convergence theorems. Our theorems improve and unify most of the results that have been proved in this direction for this important class of nonlinear mappings. Furthermore, our technique of proof is of independent interest.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Journal of Nonlinear Sciences and Applications MATHEMATICS, APPLIED-MATHEMATICS

自引率

0.00%

发文量

期刊介绍： The Journal of Nonlinear Science and Applications (JNSA) (print: ISSN 2008-1898 online: ISSN 2008-1901) is an international journal which provides very fast publication of original research papers in the fields of nonlinear analysis. Journal of Nonlinear Science and Applications is a journal that aims to unite and stimulate mathematical research community. It publishes original research papers and survey articles on all areas of nonlinear analysis and theoretical applied nonlinear analysis. All articles are fully refereed and are judged by their contribution to advancing the state of the science of mathematics. Manuscripts are invited from academicians, research students, and scientists for publication consideration. Papers are accepted for editorial consideration through online submission with the understanding that they have not been published, submitted or accepted for publication elsewhere.