希尔伯特空间中哈默斯坦积分结论近似解的惯性型算法

Fixed Point Theory and Applications Pub Date : 2021-03-29 DOI:10.1186/s13663-021-00691-7

A. U. Bello, M. T. Omojola, J. Yahaya

{"title":"希尔伯特空间中哈默斯坦积分结论近似解的惯性型算法","authors":"A. U. Bello, M. T. Omojola, J. Yahaya","doi":"10.1186/s13663-021-00691-7","DOIUrl":null,"url":null,"abstract":"Let H be a real Hilbert space. Let $F:H\\rightarrow 2^{H}$ and $K:H\\rightarrow 2^{H}$ be two maximal monotone and bounded operators. Suppose the Hammerstein inclusion $0\\in u+KFu$ has a solution. We construct an inertial-type algorithm and show its strong convergence to a solution of the inclusion. As far as we know, this is the first inertial-type algorithm for Hammerstein inclusions in Hilbert spaces. We also give numerical examples to compare the new algorithm with some existing ones in the literature.","PeriodicalId":12293,"journal":{"name":"Fixed Point Theory and Applications","volume":"27 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2021-03-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"An inertial-type algorithm for approximation of solutions of Hammerstein integral inclusions in Hilbert spaces\",\"authors\":\"A. U. Bello, M. T. Omojola, J. Yahaya\",\"doi\":\"10.1186/s13663-021-00691-7\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Let H be a real Hilbert space. Let $F:H\\\\rightarrow 2^{H}$ and $K:H\\\\rightarrow 2^{H}$ be two maximal monotone and bounded operators. Suppose the Hammerstein inclusion $0\\\\in u+KFu$ has a solution. We construct an inertial-type algorithm and show its strong convergence to a solution of the inclusion. As far as we know, this is the first inertial-type algorithm for Hammerstein inclusions in Hilbert spaces. We also give numerical examples to compare the new algorithm with some existing ones in the literature.\",\"PeriodicalId\":12293,\"journal\":{\"name\":\"Fixed Point Theory and Applications\",\"volume\":\"27 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2021-03-29\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Fixed Point Theory and Applications\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1186/s13663-021-00691-7\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Fixed Point Theory and Applications","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1186/s13663-021-00691-7","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

让 H 是一个实希尔伯特空间。让 $F:H\rightarrow 2^{H}$ 和 $K:H\rightarrow 2^{H}$ 是两个最大单调且有界的算子。假设哈默斯坦包容 $0\in u+KFu$ 有一个解。我们构建了一种惯性型算法，并证明了它对包含解的强收敛性。据我们所知，这是第一个针对希尔伯特空间中哈默斯坦包容的惯性型算法。我们还给出了数值示例，将新算法与文献中的一些现有算法进行比较。

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

微信好友朋友圈 QQ好友复制链接

本刊更多论文

An inertial-type algorithm for approximation of solutions of Hammerstein integral inclusions in Hilbert spaces

Let H be a real Hilbert space. Let $F:H\rightarrow 2^{H}$ and $K:H\rightarrow 2^{H}$ be two maximal monotone and bounded operators. Suppose the Hammerstein inclusion $0\in u+KFu$ has a solution. We construct an inertial-type algorithm and show its strong convergence to a solution of the inclusion. As far as we know, this is the first inertial-type algorithm for Hammerstein inclusions in Hilbert spaces. We also give numerical examples to compare the new algorithm with some existing ones in the literature.

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

Fixed Point Theory and Applications MATHEMATICS, APPLIED-MATHEMATICS

自引率

0.00%

发文量

期刊介绍： In a wide range of mathematical, computational, economical, modeling and engineering problems, the existence of a solution to a theoretical or real world problem is equivalent to the existence of a fixed point for a suitable map or operator. Fixed points are therefore of paramount importance in many areas of mathematics, sciences and engineering. The theory itself is a beautiful mixture of analysis (pure and applied), topology and geometry. Over the last 60 years or so, the theory of fixed points has been revealed as a very powerful and important tool in the study of nonlinear phenomena. In particular, fixed point techniques have been applied in such diverse fields as biology, chemistry, physics, engineering, game theory and economics. In numerous cases finding the exact solution is not possible; hence it is necessary to develop appropriate algorithms to approximate the requested result. This is strongly related to control and optimization problems arising in the different sciences and in engineering problems. Many situations in the study of nonlinear equations, calculus of variations, partial differential equations, optimal control and inverse problems can be formulated in terms of fixed point problems or optimization.