The Stability of a General Sextic Functional Equation by Fixed Point Theory

Abstract

In this paper, we will consider the generalized sextic functional equation ∑ i = 0 7 7 C i − 1 7 − i f x + i y = 0 . And by applying the fixed point theorem in the sense of C a ˘ dariu and Radu, we will discuss the stability of the solutions for this functional equation.

Nearly General Septic Functional Equation

“…Also, by fixed point theorem, Roh et al [24] showed the stability of the general sextic functional equation for the mapping f such that Df x, y ð Þ= 〠 7 i=0…”

“…For a number of years now, many interesting results of the stability problems to several functional equations (or involving the range from additive functional equation to sextic functional equation) have been investigated; see, e.g., [11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26].…”

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

“…Moreover, the stability of a general quintic functional equation has been studied by S. S. Jin et al [24], and the stability of the general sextic function equation has been obtained by Y. H. Lee [25], I. S, Chang et al [26], and J. Roh et al [27].…”