Aizat Toigonbaeva, A. Asanov, A. Kambarova, G. Obodoeva, U. Moldoyarov, A. Toktorbaev, Aichurok Abdukadyr Kyzy, Zhypargul D. Abdullaeva
{"title":"Uniqueness of the Fredholm-Stiltjes Linear Integral Equations Solutions of the Third Kind","authors":"Aizat Toigonbaeva, A. Asanov, A. Kambarova, G. Obodoeva, U. Moldoyarov, A. Toktorbaev, Aichurok Abdukadyr Kyzy, Zhypargul D. Abdullaeva","doi":"10.4236/alamt.2021.114008","DOIUrl":null,"url":null,"abstract":"Integral equations theoretical parts and applications have been studied and investigated in previous works. In this work, results on investigations of the uniqueness of the Fredholm-Stiltjes linear integral equations solutions of the third kind were considered. Volterra integral equations of the first and third kind with smooth kernels were studied, and proof of the existence of a multiparameter family of solutions is described. Additionally, linear Fredholm integral equations of the first kind were investigated, for which Lavrent’ev regularizing operators were constructed.","PeriodicalId":65610,"journal":{"name":"线性代数与矩阵理论研究进展(英文)","volume":"61 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"线性代数与矩阵理论研究进展(英文)","FirstCategoryId":"1089","ListUrlMain":"https://doi.org/10.4236/alamt.2021.114008","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
Integral equations theoretical parts and applications have been studied and investigated in previous works. In this work, results on investigations of the uniqueness of the Fredholm-Stiltjes linear integral equations solutions of the third kind were considered. Volterra integral equations of the first and third kind with smooth kernels were studied, and proof of the existence of a multiparameter family of solutions is described. Additionally, linear Fredholm integral equations of the first kind were investigated, for which Lavrent’ev regularizing operators were constructed.