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 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).

Representation and Stability of General Nonic Functional Equation

“…In the papers [16,[25][26][27][28][29][30][31][32][33], one can find hyperstability results for various types of functional equation. Recent results regarding the stability of the functional equation described in Equation (1) with n < 9 can be found in [34][35][36][37][38][39], and hyperstability results for this functional equation with n < 9 can be found in [38,40]. Note that the superstability of a functional equation requires that any mapping satisfying the equation approximately (in some sense) must be either a real solution to it or a bounded mapping, while hyperstability requires that any mapping satisfying the equation approximately (in some sense) must be a real solution to it.…”

Hyers-Ulam-Rassias Stability of a General Septic Functional Equation

“…in the sense of Hyers-Ulam-Rassias. Prior to this paper, in [28], I. S, Chang et al used the method of Gȃvruta to prove the stability of a general septic functional equation, i.e., if the function f : V → Y satisfies the inequality…”

Orthogonally C∗‐Ternary Jordan Homomorphisms and Jordan Derivations: Solution and Stability

“…In 1987, Rassias [3] proved a generalized version of the Hyers' theorem for approximately additive maps. Te study of stability problem of functional equations have been done by several authors on diferent spaces such as Banach, C * -Banach algebras and modular spaces (for example see [4][5][6][7][8][9][10][11][12][13]). One of the stimulating aspects is to examine the stability of those functional equations whose general solutions exist and are useful in characterizing entropies [14].…”