Fuzzy Stability of Quadratic Functional Equations

Abstract

The fuzzy stability problems for the Cauchy additive functional equation and the Jensen additive functional equation in fuzzy Banach spaces have been investigated by Moslehian et al. In this paper, we prove the generalized Hyers-Ulam stability of the following quadratic functional equations f x y f x −y 2f x 2f y and f ax by f ax −by 2a 2 f x 2b 2 f y a, b ∈ R\{0}, a / ± 1 in fuzzy Banach spaces.

Lipschitz Criteria for Bi-Quadratic Functional Equations

“…In Lipschitz spaces we investigated the stability of cubic functional equations [7] (see also [3]) and the stability of quartic functional equations [8]. On the other hand, the stability problem for the quadratic and quartic functional equation has been studied by many mathematicians under various degrees of generality imposed on the equation or on the underlying space; see, for example, [5], [6], [11] and the references therein. Park et al [10] verified the generalized Hyers-Ulam stability of the biquadratic functional equations in quasinormed spaces.…”

A fixed point approach to the stability of a septic functional equation in fuzzy quasi-β-normed spaces

“…And then, further researches related to the stability of Jensen functional equation have been considered by different authors [7,18]. In 2010, Lee et al [12] proved the generalized stability of two types of quadratic functional equations in fuzzy Banach spaces.…”