On generalized {\Phi}-strongly monotone mappings and algorithms for the solution of equations of Hammerstein type

M. Aibinu, O. Mewomo
{"title":"On generalized {\\Phi}-strongly monotone mappings and algorithms for the solution of equations of Hammerstein type","authors":"M. Aibinu, O. Mewomo","doi":"10.22075/ijnaa.2019.16797.1894","DOIUrl":null,"url":null,"abstract":"In this paper, we consider the class of generalized {\\Phi}-strongly monotone mappings and the methods of approximating a solution of equations of Hammerstein type. Auxiliary mapping is defined for nonlinear integral equations of Hammerstein type. The auxiliary mapping is the composition of bounded generalized {\\Phi}-strongly monotone mappings which satisfy the range condition. Suitable conditions are imposed to obtain the boundedness and to show that the auxiliary mapping is a generalized {\\Phi}-strongly which satisfies the range condition. A sequence is constructed and it is shown that it converges strongly to a solution of equations of Hammerstein type. The results in this paper improve and extend some recent corresponding results on the approximation of a solution of equations of Hammerstein type.","PeriodicalId":8426,"journal":{"name":"arXiv: Functional Analysis","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2020-08-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv: Functional Analysis","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.22075/ijnaa.2019.16797.1894","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0

Abstract

In this paper, we consider the class of generalized {\Phi}-strongly monotone mappings and the methods of approximating a solution of equations of Hammerstein type. Auxiliary mapping is defined for nonlinear integral equations of Hammerstein type. The auxiliary mapping is the composition of bounded generalized {\Phi}-strongly monotone mappings which satisfy the range condition. Suitable conditions are imposed to obtain the boundedness and to show that the auxiliary mapping is a generalized {\Phi}-strongly which satisfies the range condition. A sequence is constructed and it is shown that it converges strongly to a solution of equations of Hammerstein type. The results in this paper improve and extend some recent corresponding results on the approximation of a solution of equations of Hammerstein type.
关于广义{\Phi}-强单调映射和Hammerstein型方程解的算法
本文研究了一类广义{\Phi}-强单调映射及其近似Hammerstein型方程解的方法。定义了Hammerstein型非线性积分方程的辅助映射。辅助映射是有界广义{\Phi}-满足值域条件的强单调映射的复合。给出了适当的条件来获得辅助映射的有界性,并证明了辅助映射是一个广义{\Phi}-强映射,它满足值域条件。构造了一个序列,并证明了它强收敛于Hammerstein型方程的解。本文的结果改进和推广了最近关于Hammerstein型方程解近似的一些相应结果。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
求助全文
约1分钟内获得全文 求助全文
来源期刊
自引率
0.00%
发文量
0
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
确定
请完成安全验证×
copy
已复制链接
快去分享给好友吧!
我知道了
右上角分享
点击右上角分享
0
联系我们:info@booksci.cn Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术官方微信