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).