Functional equations on semigroups with an endomorphism

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• 作者：B. Fadli ; S. Kabbaj ; KH. Sabour ; D. Zeglami
• 关键词：Key words and phrasesfunctional equation ; d’Alembert ; Jensen ; multiplicative function ; additive map ; semigroup ; endomorphism
• 刊名：Acta Mathematica Hungarica
• 出版年：2016
• 出版时间：December 2016
• 年：2016
• 卷：150
• 期：2
• 页码：363-371
• 全文大小：477 KB
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Sciences
  Mathematics
  
• 出版者：Akad茅miai Kiad贸, co-published with Springer Science+Business Media B.V., Formerly Kluwer Academic
• ISSN：1588-2632
• 卷排序：150

文摘

Let S be a semigroup, let H be an abelian group which is 2-torsion free, and let \({\varphi \colon S \to S}\) be an endomorphism. We determine the solutions \({ g \colon S \to \mathbb{C}}\) of the functional equation$$g(xy)+g(\varphi(y)x)=2g(x)g(y), \quad x,y \in S,$$in terms of multiplicative functions on S, and we show that any solution \({ {g \colon S\to H }}\), when \({\varphi}\) is surjective, of the functional equation$$g(xy)+g(\varphi(y)x)=2g(x), \quad x,y \in S,$$has the form \({g=A+c }\), where \({A \colon S\rightarrow H}\) is an additive map such that \({{ A\circ\varphi =-A }}\), and where \({c\in H}\) is a constant. The endomorphism \({ \varphi}\) need not be involutive.Key words and phrasesfunctional equationd’AlembertJensenmultiplicative functionadditive mapsemigroupendomorphismMathematics Subject Classification39B3239B52References1.Aczél J., Dhombres J.: Functional Equations in Several Variables. 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Fadli, Integral functional equations on locally compact groups with involution, Aequationes Math., (2016), DOI:10.1007/s00010-016-0417-z.Copyright information© Akadémiai Kiadó, Budapest, Hungary 2016Authors and AffiliationsB. Fadli1S. Kabbaj1KH. Sabour1D. Zeglami2Email author1.Department of Mathematics, Faculty of SciencesIbn Tofail UniversityKenitraMorocco2.Department of MathematicsE.N.S.A.M, Moulay Ismail UniversityAl MansurMorocco About this article CrossMark Print ISSN 0236-5294 Online ISSN 1588-2632 Publisher Name Springer Netherlands 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/s10474-016-0635-9_Functional equations on semigroups", 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/s10474-016-0635-9_Functional equations on semigroups", 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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