Wilson’s functional equation on monoids with involutive automorphisms

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• 作者：Kh. Sabour ; B. Fadli ; S. Kabbaj
• 关键词：Functional equation ; involutive automorphism ; Wilson ; Monoid ; multiplicative function
• 刊名：Aequationes Mathematicae
• 出版年：2016
• 出版时间：October 2016
• 年：2016
• 卷：90
• 期：5
• 页码：1001-1011
• 全文大小：441 KB
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Analysis
  Combinatorics
  
• 出版者：Birkh盲user Basel
• ISSN：1420-8903
• 卷排序：90

文摘

In the present paper, we determine the complex-valued solutions (f, g) of the functional equation$$f(x\sigma(y))+f(\tau(y)x)=2f(x)g(y),$$in the setting of groups and monoids that need not be abelian, where \({\sigma,\tau}\) are involutive automorphisms. We prove that their solutions can be expressed in terms of multiplicative and additive functions.KeywordsFunctional equationinvolutive automorphismWilsonMonoidmultiplicative functionMathematics Subject ClassificationPrimary 39B3239B52References1.d’Alembert J.: Addition au Mémoire sur la courbe que forme une corde tendue mise en vibration. Hist. Acad. Berl. 1750, 355–360 (1750)Google Scholar2.Cauchy, A.L.: Cours d’Analyse de l’Ecole Polytechnique, vol. 1. Analyse algebrique, V., Paris (1821)3.Chahbi, A., Fadli, B., Kabbaj, S.: A generalization of the symmetrized multiplicative Cauchy equation. Acta Math. Hung. 149(1), 170–176 (2016)MathSciNetCrossRefGoogle Scholar4.Ebanks B.R., Stetkær H.: d’Alembert’s other functional equation on monoids with an involution. Aequ. Math. 89, 187–206 (2015)CrossRefMATHGoogle Scholar5.Ebanks B.R., Stetkær H.: On Wilson’s functional equations. Aequ. Math. 89(2), 339–354 (2015)CrossRefMATHGoogle Scholar6.Fadli, B., Zeglami, D., Kabbaj, S.: A variant of Wilson’s functional equation. Publ. Math. Debr. 87(3–4), 415–427 (2015)MathSciNetCrossRefMATHGoogle Scholar7.Kannappan P.L.: Functional Equations and Inequalities with Applications. Springer, New York (2009)CrossRefMATHGoogle Scholar8.Stetkær H.: Functional equations on abelian groups with involution. Aequ. Math. 54, 144–172 (1997)MathSciNetCrossRefMATHGoogle Scholar9.Stetkær H.: Functional Equations on Groups. World Scientific Publishing Co, Singapore (2013)CrossRefMATHGoogle Scholar10.Stetkær H.: A variant of d’Alembert’s functional equation. Aequ. Math. 89, 657–662 (2015)CrossRefMATHGoogle Scholar11.Wilson, W.H.: On certain related functional equations. Bull. Am. Math. Soc. 26, 300–312 (1919–1920) [Fortschr. 47, 320 (1919–1920)]Copyright information© Springer International Publishing 2016Authors and AffiliationsKh. Sabour1B. Fadli1Email authorS. Kabbaj11.Department of Mathematics, Faculty of SciencesIbn Tofail UniversityKenitraMorocco About this article CrossMark Print ISSN 0001-9054 Online ISSN 1420-8903 Publisher Name Springer International Publishing 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/s00010-016-0435-x_Wilson’s functional equation on mo", 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/s00010-016-0435-x_Wilson’s functional equation on mo", 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. More information Accept Over 10 million scientific documents at your fingertips