Fuzzy Stability of Quadratic Functional Equations in General Cases

Abstract

The aim of this paper is to investigate fuzzy Hyers-Ulam-Rassias stability of the general case of quadratic functional equation where and fixed integers with . These functional equations are equivalent. This has been proven by Ulam, 1964.

Hyers Stability and Multi-Fuzzy Banach Algebra

“…Mathematicians developed the results of the Hyers theorem. By changing the space, the norm, the control function, and functional equation, they could prove more interesting theorems [7][8][9][10][11][12][13][14]. For example, the Jenson functional equation or the integral and differential equations were used instead of the functional equation (in the theorem) and the validity of the theorem was proved.…”

Stability of a generalized quadratic functional equation in intuitionistic fuzzy 2-normed space

“…Recently, considerable attention has been increasing to the problem of fuzzy stability of functional equations. Several various fuzzy stability results concerning Cauchy, Jensen, simple quadratic, and cubic functional equations have been investigated [1,6,11,23,31] Quite recently, the stability results in the setting of intuitionistic fuzzy normed space were studied in [7,[18][19][20]22]respectively, while the idea of intuitionistic fuzzy normed space was introduced in [25].…”