A note on the Hyers-Ulam-Rassias stability of a quadratic equation
Bull. Korean Math. Soc. 2004 Vol. 41, No. 3, 541-557
Published online September 1, 2004
Jie-Hyung Kang, Chang-Ju Lee, and Yang-Hi Lee
Kongju National University of Education, Kongju National University of Education
Abstract : In this paper we prove the Hyers-Ulam-Rassias stability by considering the cases that the approximate remainder $\varphi$ is defined by $f(x*y)+f(x*y^{-1})-2f(x)-2f(y)= \varphi(x,y)$, $f(x*y*z)+f(x)+f(y)+f(z)-f(x*y)-f(y*z)-f(z*x)=\varphi(x,y,z)$, where $(G,*)$ is a group, $X$ is a real or complex Hausdorff topological vector space, and $f$ is a function from $G$ into $X$.
Keywords : quadratic function
MSC numbers : Primary 39B72, 47H15
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