拆分变分包含与不动点问题的自适应惯性Yosida逼近迭代算法

IF 1.8 3区数学 Q1 MATHEMATICS

AIMS Mathematics Pub Date : 2023-01-01 DOI:10.3934/math.2023651

M. Dilshad, M. Akram, M. Nasiruzzaman, D. Filali, A. Khidir

{"title":"拆分变分包含与不动点问题的自适应惯性Yosida逼近迭代算法","authors":"M. Dilshad, M. Akram, M. Nasiruzzaman, D. Filali, A. Khidir","doi":"10.3934/math.2023651","DOIUrl":null,"url":null,"abstract":"In this paper, we present self-adaptive inertial iterative algorithms involving Yosida approximation to investigate a split variational inclusion problem (SVIP) and common solutions of a fixed point problem (FPP) and SVIP in Hilbert spaces. We analyze the weak convergence of the proposed iterative algorithm to explore the approximate solution of the SVIP and strong convergence to estimate the common solution of the SVIP and FPP under some mild suppositions. A numerical example is demonstrated to validate the theoretical findings, and comparison of our iterative methods with some known schemes is outlined.","PeriodicalId":48562,"journal":{"name":"AIMS Mathematics","volume":null,"pages":null},"PeriodicalIF":1.8000,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"Adaptive inertial Yosida approximation iterative algorithms for split variational inclusion and fixed point problems\",\"authors\":\"M. Dilshad, M. Akram, M. Nasiruzzaman, D. Filali, A. Khidir\",\"doi\":\"10.3934/math.2023651\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this paper, we present self-adaptive inertial iterative algorithms involving Yosida approximation to investigate a split variational inclusion problem (SVIP) and common solutions of a fixed point problem (FPP) and SVIP in Hilbert spaces. We analyze the weak convergence of the proposed iterative algorithm to explore the approximate solution of the SVIP and strong convergence to estimate the common solution of the SVIP and FPP under some mild suppositions. A numerical example is demonstrated to validate the theoretical findings, and comparison of our iterative methods with some known schemes is outlined.\",\"PeriodicalId\":48562,\"journal\":{\"name\":\"AIMS Mathematics\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":1.8000,\"publicationDate\":\"2023-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"AIMS Mathematics\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.3934/math.2023651\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"AIMS Mathematics","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.3934/math.2023651","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}

引用次数: 1

摘要

本文提出了包含Yosida近似的自适应惯性迭代算法来研究Hilbert空间中的分裂变分包含问题(SVIP)以及不动点问题(FPP)和SVIP的公共解。我们分析了所提出的迭代算法的弱收敛性，以探索SVIP的近似解，以及在一些温和假设下估计SVIP和FPP的公解的强收敛性。通过数值算例验证了理论结果，并与一些已知方案进行了比较。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

Adaptive inertial Yosida approximation iterative algorithms for split variational inclusion and fixed point problems

In this paper, we present self-adaptive inertial iterative algorithms involving Yosida approximation to investigate a split variational inclusion problem (SVIP) and common solutions of a fixed point problem (FPP) and SVIP in Hilbert spaces. We analyze the weak convergence of the proposed iterative algorithm to explore the approximate solution of the SVIP and strong convergence to estimate the common solution of the SVIP and FPP under some mild suppositions. A numerical example is demonstrated to validate the theoretical findings, and comparison of our iterative methods with some known schemes is outlined.

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

AIMS Mathematics Mathematics-General Mathematics

CiteScore

3.40

自引率

13.60%

发文量

769

审稿时长

90 days

期刊介绍： AIMS Mathematics is an international Open Access journal devoted to publishing peer-reviewed, high quality, original papers in all fields of mathematics. We publish the following article types: original research articles, reviews, editorials, letters, and conference reports.