多变量一般泛函方程系统的微扰

IF 1.3 3区数学 Q2 MATHEMATICS, APPLIED

Bulletin des Sciences Mathematiques Pub Date : 2025-03-31 DOI:10.1016/j.bulsci.2025.103624

Hamid Khodaei

{"title":"多变量一般泛函方程系统的微扰","authors":"Hamid Khodaei","doi":"10.1016/j.bulsci.2025.103624","DOIUrl":null,"url":null,"abstract":"<div><div>Pólya and Szegő <span><span>[53, Teil I, Aufgabe 99]</span></span> proved that every approximate sequence of reals is near an additive sequence. Bourgin <span><span>[11]</span></span> showed that every approximate ring homomorphism from a Banach algebra onto a unital Banach algebra is necessarily a ring homomorphism. We deal with Pólya-Szegő's result for a general functional equation and a system of general functional equations in several variables. To do this, we shall use a different direct method from the previous studies. In consequence, Bourgin's result for approximate homomorphisms and Lie homomorphisms on Banach algebras are discussed. Several examples for comparison with previous studies are included.</div></div>","PeriodicalId":55313,"journal":{"name":"Bulletin des Sciences Mathematiques","volume":"202 ","pages":"Article 103624"},"PeriodicalIF":1.3000,"publicationDate":"2025-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Perturbations of a system of general functional equations in several variables\",\"authors\":\"Hamid Khodaei\",\"doi\":\"10.1016/j.bulsci.2025.103624\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><div>Pólya and Szegő <span><span>[53, Teil I, Aufgabe 99]</span></span> proved that every approximate sequence of reals is near an additive sequence. Bourgin <span><span>[11]</span></span> showed that every approximate ring homomorphism from a Banach algebra onto a unital Banach algebra is necessarily a ring homomorphism. We deal with Pólya-Szegő's result for a general functional equation and a system of general functional equations in several variables. To do this, we shall use a different direct method from the previous studies. In consequence, Bourgin's result for approximate homomorphisms and Lie homomorphisms on Banach algebras are discussed. Several examples for comparison with previous studies are included.</div></div>\",\"PeriodicalId\":55313,\"journal\":{\"name\":\"Bulletin des Sciences Mathematiques\",\"volume\":\"202 \",\"pages\":\"Article 103624\"},\"PeriodicalIF\":1.3000,\"publicationDate\":\"2025-03-31\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Bulletin des Sciences Mathematiques\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0007449725000508\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Bulletin des Sciences Mathematiques","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0007449725000508","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}

引用次数: 0

摘要

Pólya和szegov [53， Teil I， Aufgabe 99]证明了实数的每一个近似序列都接近于一个加性序列。Bourgin[11]证明了从Banach代数到一元Banach代数的每一个近似环同态必然是环同态。我们处理一个一般泛函方程和一个多变量的一般泛函方程组的Pólya-Szegő的结果。为了做到这一点，我们将使用与以前的研究不同的直接方法。因此，讨论了关于Banach代数上的近似同态和Lie同态的Bourgin结果。文中还列举了几个与以往研究相比较的例子。

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

Perturbations of a system of general functional equations in several variables

Pólya and Szegő [53, Teil I, Aufgabe 99] proved that every approximate sequence of reals is near an additive sequence. Bourgin [11] showed that every approximate ring homomorphism from a Banach algebra onto a unital Banach algebra is necessarily a ring homomorphism. We deal with Pólya-Szegő's result for a general functional equation and a system of general functional equations in several variables. To do this, we shall use a different direct method from the previous studies. In consequence, Bourgin's result for approximate homomorphisms and Lie homomorphisms on Banach algebras are discussed. Several examples for comparison with previous studies are included.

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