Hyers–Ulam stability of a functional equation with several parameters

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• 作者：Lahbib Oubbi
• 关键词：Hyers–Ulam stability ; Functional equation ; Ring homomorphisms ; Ring n ; derivations
• 刊名：Afrika Matematika
• 出版年：2016
• 出版时间：December 2016
• 年：2016
• 卷：27
• 期：7-8
• 页码：1199-1212
• 全文大小：457 KB
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics Education
  Applications of Mathematics
  History of Mathematics
  Mathematics
  
• 出版者：Springer Berlin / Heidelberg
• ISSN：2190-7668
• 卷排序：27

文摘

We consider the functional equation: $$\begin{aligned} \sum _{i=1}^{m}f(a_i x_0 + b_i x_i) + f\left( x_0 - \sum _{i=1}^{m}b_i x_i\right) = f(x_0), \end{aligned}$$ (1)where \(m \ge 2\) is an integer, \((a_i)_{i=1, \dots , m}\) and \((b_i)_{i=1, \dots , m}\) are scalars so that \(\sum _{i=1}^m a_i = 0\) and \(b_i \ne 0\) for every \(i = 1, \dots , m\). We prove the Hyers–Ulam stability of (1) under several kinds of approximation conditions and with different methods. Unlike most of authors, when using the fixed point theorem method, we use the classical Banach contraction principle instead of the alternative fixed point theorem. We then combine (1) with some other equations and show the stability of the obtained systems. 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Wiley, New York (1940)MATHGoogle ScholarCopyright information© African Mathematical Union and Springer-Verlag Berlin Heidelberg 2016Authors and AffiliationsLahbib Oubbi1Email author1.Mohammed V University of Rabat, Ecole Normale SupérieureRabatMorocco About this article CrossMark Print ISSN 1012-9405 Online ISSN 2190-7668 Publisher Name Springer Berlin Heidelberg About this journal Reprints and Permissions Article actions function trackAddToCart() { var buyBoxPixel = new webtrekkV3({ trackDomain: "springergmbh01.webtrekk.net", trackId: "196033507532344", domain: "link.springer.com", contentId: "springer_com.buybox", product: "10.1007/s13370-016-0403-6_Hyers–Ulam stability of a function", productStatus: "add", productCategory : { 1 : "ppv" }, customEcommerceParameter : { 9 : "link.springer.com" } }); buyBoxPixel.sendinfo(); } function trackSubscription() { var subscription = new webtrekkV3({ trackDomain: "springergmbh01.webtrekk.net", trackId: "196033507532344", domain: "link.springer.com", contentId: "springer_com.buybox" }); subscription.sendinfo({linkId: "inst. subscription info"}); } window.addEventListener("load", function(event) { var viewPage = new webtrekkV3({ trackDomain: "springergmbh01.webtrekk.net", trackId: "196033507532344", domain: "link.springer.com", contentId: "SL-article", product: "10.1007/s13370-016-0403-6_Hyers–Ulam stability of a function", productStatus: "view", productCategory : { 1 : "ppv" }, customEcommerceParameter : { 9 : "link.springer.com" } }); viewPage.sendinfo(); }); Log in to check your access to this article Buy (PDF)EUR 34,95 Unlimited access to full article Instant download (PDF) Price includes local sales tax if applicable Find out about institutional subscriptions Export citation .RIS Papers Reference Manager RefWorks Zotero .ENW EndNote .BIB BibTeX JabRef Mendeley Share article Email Facebook Twitter LinkedIn Cookies We use cookies to improve your experience with our site. 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