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 G $\breve{\text{a}}$ vruta, we examine the stability of general septic functional equation ${\sum }_{i=0}^8{{}_{8}C}_i{\left(-1\right)}^{8-i}f\left(x+\left(i-4\right)y\right)=0$ which considered. The method of G $\breve{\text{a}}$ vruta as just mentioned was given in the reference Gavruta (1994).