won{gil park [won{gil park, j. math. anal. appl., 376 (1) (2011) 193{202] proved the hyers{ulam stability of the cauchy functional equation, the jensen functional equation and the quadraticfunctional equation in 2{banach spaces. one can easily see that all results of this paper are incorrect.hence the control functions in all theorems of this paper are not correct. in this paper, we correctthes...

In this paper, using the fixed point and direct methods, we prove the generalized Hyers-Ulam-Rassias stability of the following Cauchy-Jensen additive functional equation: begin{equation}label{main} fleft(frac{x+y+z}{2}right)+fleft(frac{x-y+z}{2}right)=f(x)+f(z)end{equation} in various normed spaces. The concept of Hyers-Ulam-Rassias stability originated from Th. M. Rassias’ stability theorem t...

* Correspondence: baak@hanyang. ac.kr Department of Mathematics, Research Institute for Natural Sciences, Hanyang University, Seoul 133-791, South Korea Full list of author information is available at the end of the article Abstract Using the fixed point method, we prove the Hyers-Ulam stability of a Cauchy-Jensen type additive set-valued functional equation, a Jensen type additive-quadratic se...

in the present paper a solution of the generalizedquadratic functional equation$$f(kx+ y)+f(kx+sigma(y))=2k^{2}f(x)+2f(y),phantom{+} x,yin{e}$$ isgiven where $sigma$ is an involution of the normed space $e$ and$k$ is a fixed positive integer. furthermore we investigate thehyers-ulam-rassias stability of the functional equation. thehyers-ulam stability on unbounded domains is also studied.applic...

Let Q be a positive definite integral quadratic form in ti variables, with the additional property that the adjoint form Q' is also integral. Using the functional equation of the Epstein zeta function, we obtain a symmetric functional equation of the ¿-function of Q with a primitive character to mod q (additive or multiplicative) defined by £io(2(x))C(x)-ï. Re(s) > nl2> where the summation exte...