2 - Variable AQCQ - Functional equation - Arunkuma, M.; Hema Latha, S.; Sathya, E. (International Journal of Advanced Mathematical Sciences, 2015)
In this paper, the authors obtain the general solution and generalized Ulam - Hyers stability of a 2 - variable AQCQ functional equation\begin{align*}g(x+2y, u+2v)+g(x-2y, u-2v)& = 4[g(x+y, u+v) + g(x-y, u-v)]- 6g(x,u) otag\\ &~~+g(2y,2v)+g(-2y,-2v)-4g(y,v)-4g(-y,-v)\end{align*}using Hyers direct method. Counter examples for non stability is also discussed.
Keywords: Additive functional equations; Quadratic functional equations; Cubic functional equations; Quartic functional equations; Mixed type functional equations; Ulam - Hyers stability; Ulam - Hyers - Rassias stability; Ulam - Gavruta - Rassias stability