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 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).
Highlights
The concept of stability for a functional equation arising when replacing the functional equation by an inequality which acts as a perturbation of the equation
Suppose that a function φ : V2 ⟶ 1⁄20, ∞Þ satisfies the condition for all x, y ∈ V: Assume that f : V ⟶ Y is a mapping subject to the inequality kDf ðx, yÞk ≤ φðx, yÞ, ð22Þ
We investigated the stability of general septic functional equation by using the method of Gavruta
Summary
The concept of stability for a functional equation arising when replacing the functional equation by an inequality which acts as a perturbation of the equation. Holds for all x, y ∈ G: there exists a unique additive mapping T : G ⟶ Y with kf ðxÞ Journal of Function Spaces we say that each solution of the previous equation is additive, quadratic, cubic, quartic, quintic, sextic, and septic mapping, respectively.
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