Nearly General Septic Functional Equation

If a mapping can be expressed by sum of a septic mapping, a sextic mapping, a quintic mapping, a quartic mapping, a cubic mapping, a quadratic mapping, an additive mapping, and a constant mapping, we say that it is a general septic mapping. A functional equation is said to be a general septic functional equation provided that each solution of that equation is a general septic mapping. In fact, there are a lot of ways to show the stability of functional equations, but by using the method of G a ˘ vruta, we examine the stability of general septic functional equation ∑ i = 0 8 C 8 i − 1 8 − i f x + i − 4 y = 0 which considered. The method of G a ˘ vruta as just mentioned was given in the reference Gavruta (1994).