{"title":"用Petryshyn不动点定理求解非线性Volterra积分方程的可解性及数值方法","authors":"A. Deep, Ashisha Kumar, Syed Abbas, M. Rabbani","doi":"10.22075/IJNAA.2021.22858.2422","DOIUrl":null,"url":null,"abstract":"In this paper, utilizing the technique of Petryshyn’s fixed point theorem in Banach algebra, we analyze the existence of solution for functional integral equations, which includes as special cases many functional integral equations that arise in various branches of non-linear analysis and its application. Finally, we introduce the numerical method formed by modified homotopy perturbation approach to resolving the problem with acceptable accuracy.","PeriodicalId":14240,"journal":{"name":"International Journal of Nonlinear Analysis and Applications","volume":"13 1","pages":"1-28"},"PeriodicalIF":0.0000,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":"{\"title\":\"Solvability and numerical method for non-linear Volterra integral equations by using Petryshyn’s fixed point theorem\",\"authors\":\"A. Deep, Ashisha Kumar, Syed Abbas, M. Rabbani\",\"doi\":\"10.22075/IJNAA.2021.22858.2422\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this paper, utilizing the technique of Petryshyn’s fixed point theorem in Banach algebra, we analyze the existence of solution for functional integral equations, which includes as special cases many functional integral equations that arise in various branches of non-linear analysis and its application. Finally, we introduce the numerical method formed by modified homotopy perturbation approach to resolving the problem with acceptable accuracy.\",\"PeriodicalId\":14240,\"journal\":{\"name\":\"International Journal of Nonlinear Analysis and Applications\",\"volume\":\"13 1\",\"pages\":\"1-28\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2022-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"2\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"International Journal of Nonlinear Analysis and Applications\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.22075/IJNAA.2021.22858.2422\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"Mathematics\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"International Journal of Nonlinear Analysis and Applications","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.22075/IJNAA.2021.22858.2422","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"Mathematics","Score":null,"Total":0}
Solvability and numerical method for non-linear Volterra integral equations by using Petryshyn’s fixed point theorem
In this paper, utilizing the technique of Petryshyn’s fixed point theorem in Banach algebra, we analyze the existence of solution for functional integral equations, which includes as special cases many functional integral equations that arise in various branches of non-linear analysis and its application. Finally, we introduce the numerical method formed by modified homotopy perturbation approach to resolving the problem with acceptable accuracy.
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