On the Hyers-Ulam-Rassias Stability of an Additive-cubic-quartic Functional Equation
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In this paper, we investigate Hyers-Ulam-Rassias stability of the functional equation \begin{align*} f(x+ky) & - k^2 f(x+y)+2(k^2-1)f(x)- k^2 f(x-y)+ f(x-ky)\nonumber \\ & - k^2(k^2 -1)(f(y) + f(-y))=0. %\\ f(x+2y) & - 4 f(x+y)+ 6f(x)- 4 f(x-y)+ f(x-2y)\nonumber % \\ & - f(2y)-f(-2y) + 4 f(y)+ 4 f(-y)=0, \end{align*} where $k$ is a fixed real number with $k \not\in \{ 0, 1,-1 \}$
Abstract
In this paper, we investigate Hyers-Ulam-Rassias stability of the functional equation \begin{align*} f(x+ky) & - k^2 f(x+y)+2(k^2-1)f(x)- k^2 f(x-y)+ f(x-ky)\nonumber \\ & - k^2(k^2 -1)(f(y) + f(-y))=0. %\\ f(x+2y) & - 4 f(x+y)+ 6f(x)- 4 f(x-y)+ f(x-2y)\nonumber % \\ & - f(2y)-f(-2y) + 4 f(y)+ 4 f(-y)=0, \end{align*} where $k$ is a fixed real number with $k \not\in \{ 0, 1,-1 \}$
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