Hyperstability of an n-dimensional Jensen type functional equation

详细信息    查看全文

• 作者：Iz-iddine EL-Fassi
• 关键词：Hyperstability ; Jensen functional equation ; Fixed point theorem
• 刊名：Afrika Matematika
• 出版年：2016
• 出版时间：December 2016
• 年：2016
• 卷：27
• 期：7-8
• 页码：1377-1389
• 全文大小：428 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

In this paper, we will investigate some hyperstability results of an n-dimensional Jensen type functional equation $$\begin{aligned} \sum _{i=1}^{n} p_{i} f(x_{i})=f\left( \sum _{i=1}^{n} p_{i} x_{i}\right) , \end{aligned}$$where \(n>1\) is an integer, and \(p_{1},\ldots ,p_{n}\) are positive rational numbers with $$\begin{aligned} \sum _{i=1}^{n} p_{i}=1. \end{aligned}$$KeywordsHyperstabilityJensen functional equationFixed point theoremMathematical Subject ClassificationPrimary 39B8239B62Secondary 47J2047H10References1.Aoki, T.: On the stability of the linear transformation in Banach spaces. J. Math. Soc. Jpn. 2, 64–66 (1950)MathSciNetCrossRefMATHGoogle Scholar2.Bahyrycz, A., Piszczek, M.: Hyperstability of the Jensen functional equation. Acta Math. Hung. 142(2), 353–365 (2014)MathSciNetCrossRefMATHGoogle Scholar3.Bourgin, D.G.: Approximately isometric and multiplicative transformations on continuous function rings. Duke Math. J. 16, 385–397 (1949)MathSciNetCrossRefMATHGoogle Scholar4.Bourgin, D.G.: Classes of transformations and bordering transformations. Bull. Am. Math. Soc. 57, 223–237 (1951)MathSciNetCrossRefMATHGoogle Scholar5.Brzdek, J., Chudziak, J., Páles, Z.: A fixed point approach to stability of functional equations. Nonlinear Anal. 74(17), 6728–6732 (2011)MathSciNetCrossRefMATHGoogle Scholar6.Brzdek, J.: Remarks on hyperstability of the the Cauchy equation. Aequat. Math. 86, 255–267 (2013)MathSciNetCrossRefMATHGoogle Scholar7.Brzdek, J.: Hyperstability of the Cauchy equation on restricted domains. Acta Math. Hung. 141(1–2), 58–67 (2013)MathSciNetCrossRefGoogle Scholar8.Brzdek, J.: A hyperstability result for the Cauchy equation. Bull. Aust. Math. Soc. 89, 33–40 (2014)MathSciNetCrossRefGoogle Scholar9.Cǎdariu, L., Radu, V.: Fixed points and the stability of Jensens functional equation. J. Inequal. Pure Appl. Math. 4(1) (2003)10.EL-Fassi, Iz., Kabbaj, S.: On the hyperstability of a Cauchy-Jensen type functional equation in Banach spaces. Proyecciones J. Math. 34(4), 359–375 (2015)11.Gajda, Z.: On stability of additive mappings. Int. J. Math. Math. Sci. 14, 431–434 (1991)MathSciNetCrossRefMATHGoogle Scholar12.Gselmann, E.: Hyperstability of a functional equation. Acta Math. Hung. 124(1–2), 179–188 (2009)MathSciNetCrossRefMATHGoogle Scholar13.Hyers, D.H.: On the stability of the linear functional equation. Proc. Nat. Acad. Sci. USA, 27, 222–224 (1941)14.Tipyan, J., Srisawat, C., Udomkavanich, P., Nakmahachalasint, P.: The Generalized Stability of an n-dimensional Jensen type Functional Equation. Thai. J. Math. 12(2), 265–274 (2014)MathSciNetMATHGoogle Scholar15.Jung, S.M.: Hyers-Ulam-Rassias stability of Jensen’s equation and its application. Proc. Am. Math. Soc. 80, 411–416 (1998)MATHGoogle Scholar16.Jung, S.M., Moslehian, M.S., Sahoo, P.K.: Stability of a generalized Jensen equation on restricted domains. J. Math. Inequalities 4, 191–206 (2010)MathSciNetCrossRefMATHGoogle Scholar17.Kominek, Z.: On a local stability of the Jensen functional equation. Demonstratio Math. 22, 499–507 (1989)MathSciNetMATHGoogle Scholar18.Lee, Y.H., Jun, K.W.: A generalization of the Hyers-Ulam-Rassias stability of Jensens equation. J. Math. Anal. Appl. 238, 305–315 (1999)MathSciNetCrossRefMATHGoogle Scholar19.Maksa, G., Páles, Z.: Hyperstability of a class of linear functional equations. Acta Math. 17(2), 107–112 (2001)MathSciNetMATHGoogle Scholar20.Park, C., Rassias, J.M.: Stability of the Jensen-type functional equation in C*-algebras: a fixed point approach. Abstr. Appl. Anal. 2009, 17 (2009) (article ID 360432)21.Piszczek, M.: Remark on hyperstability of the general linear equation. Aequat. Math. (2013)22.Rassias, Th.M.: On the stability of the linear mapping in Banach spaces. Proc. Am. Math. Soc. 72, 297–300 (1978)23.Rassias, Th.M.: On a modified Hyers Ulam sequence. J. Math. Anal. Appl. 158, 106–113 (1991)24.Rassias, Th.M., Semrl, P.: On the behavior of mappings which do not satisfy Hyers-Ulam stability. Proc. Am. Math. Soc. 114, 989–993 (1992)25.Rassias, J.M.: On the Ulam stability of Jensen and Jensen type mappings on restricted domains. J. Math. Anal. Appl. 281, 516–524 (2003)MathSciNetCrossRefMATHGoogle Scholar26.Rassias, J.M., Rassias, M.J.: Asympotic behavoir of alternative Jensen and Jensen type functional equation. Bull. Sci. Math. 129, 545–558 (2005)MathSciNetCrossRefMATHGoogle Scholar27.Ulam, S.M.: Problems in modern mathematics. Chapter IV, Science editions. Wiley, New York (1960)Copyright information© African Mathematical Union and Springer-Verlag Berlin Heidelberg 2016Authors and AffiliationsIz-iddine EL-Fassi1Email author1.Department of Mathematics, Faculty of SciencesUniversity of Ibn TofailKenitraMorocco 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/s13370-016-0417-0_Hyperstability of an n-dimensional", 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/s13370-016-0417-0_Hyperstability of an n-dimensional", 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