A fixed point approach to the stability of a general mixed AQCQ-functional equation in non-Archimedean normed spaces
Summary: Using fixed point methods, we prove the generalized Hyers-Ulam stability of the general mixed additive-quadratic-cubic-quartic functional equation \[ \begin{multlined} f(x+ky)+f(x - ky)=k^{2}f(x+y)+k^{2}f(x - y)+2(1 - k^{2})f(x)\\ +\frac{k^4 - k^2}{12}[f(2y)+f( - 2y) - 4f(y) - 4f( - y)]\end{multlined} \] for a fixed integer \(k\) with \(k\neq 0,\pm \)1 in non-Archimedean normed spaces.
general mixed additive-quadratic-cubic-quartic (AQCQ) functional equation
scientific article; zbMATH DE number 5793508
scientific article