Nearly general septic functional equation (Q2064424)

Summary: 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 Găvruta, we examine the stability of general septic functional equation \(\sum_{i = 0}^8 {}_8C_i(-1)^{8-i}f(x+(i-4)y)=0\) which considered. The method of Găvruta as just mentioned was given in the reference [\textit{P. Gǎvruţa}, J. Math. Anal. Appl. 184, No. 3, 431--436 (1994; Zbl 0818.46043)].