On a new type of stability of a radical quadratic functional equation using Brzdȩk’s fixed point theorem

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• 作者：L. Aiemsomboon ; W. Sintunavarat
• 关键词：Key words and phrasesBrzdȩk’s fixed point theorem ; Hyers–Ulam stability ; radical quadratic functional equation
• 刊名：Acta Mathematica Hungarica
• 出版年：2017
• 出版时间：February 2017
• 年：2017
• 卷：151
• 期：1
• 页码：35-46
• 全文大小：
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics, general;
• 出版者：Springer Netherlands
• ISSN：1588-2632
• 卷排序：151

文摘

Using a fixed point result and an approach to stability of functional equations presented in [8], we investigate a new type of stability for the radical quadratic functional equation of the form $$ f(\sqrt{x^2+y^2}) = f(x) + f(y), $$where f is a self-mapping on the set of real numbers. We generalize, extend, and complement some earlier classical results concerning the Hyers–Ulam stability for that functional equations.Key words and phrasesBrzdȩk’s fixed point theoremHyers–Ulam stabilityradical quadratic functional equationThis work was supported by Research Professional Development Project under the Science Achievement Scholarship of Thailand (SAST).