On the stability of a radical cubic functional equation in quasi- \({\beta}\) -spaces
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In this paper, we introduce and solve the radical cubic functional equation$$f\left({\sqrt[3]{x^{3} + y^{3}}}\right)= f(x) + f(y).$$We also establish stability in quasi-\({\beta}\)-Banach spaces, and then the stability by using subadditive and subquadratic functions for the radical cubic functional equation in (\({\beta}\), p)-Banach spaces is given.KeywordsRadical functional equationsHyers–Ulam–Rassias stabilityquasi-\({\beta}\)-normed spacessubadditive and subquadratic functionsMathematics Subject Classification41A3039B5239B8246L05References1.Aoki T.: On the stability of the linear transformation in Banach spaces. J. Math. Soc. Japan 2, 64–66 (1950)MathSciNetCrossRefMATHGoogle Scholar2.Bourgin D.G.: Classes of transformations and bordering transformations. Bull. Amer. Math. Soc. 57, 223–237 (1951)MathSciNetCrossRefMATHGoogle Scholar3.Czerwik S.: On the stability of the quadratic mapping in normed spaces. Abh. Math. Semin. Univ. 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Chapter VI, Science Editions, Wiley, New York, 1964.Copyright information© Springer International Publishing 2016Authors and AffiliationsZ. Alizadeh1Email authorA. G. Ghazanfari11.Department of MathematicsLorestan UniversityKhoramabadIran About this article CrossMark Print ISSN 1661-7738 Online ISSN 1661-7746 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/s11784-016-0317-9_On the stability of a radical cubi", 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/s11784-016-0317-9_On the stability of a radical cubi", 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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