Nearly General Septic Functional Equation

Abstract

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 Ga˘vruta, we examine the stability of general septic functional equation ∑i=08C8i−18−ifx+i−4y=0 which considered. The method of Ga˘vruta as just mentioned was given in the reference Gavruta (1994).