Approximate Euler-Lagrange Quadratic Mappings in Fuzzy Banach Spaces

Abstract

We consider general solution and the generalized Hyers-Ulam stability of an Euler-Lagrange quadratic functional equation (+) + (−) = (+)[ () + ()] in fuzzy Banach spaces, where , are nonzero rational numbers with 2 + + 2 − 1 ̸ = 0, + ̸ = 0.

Stability of a functional equation related to quadratic mappings

“…H.-M. Kim and J.-R. Lee [5] showed that for fixed rational numbers a and b if f : V → W is a solution of the functional equation (1.2), then f is a quadratic mapping. In the following lemma, we get the converse of it for some conditions.…”

“…Now, in this paper, we will show that the solution of the functional equation (1.2) is a quadratic-additive mapping and investigate the stability of it. In [5], H.-K. Kim…”

Approximate Homomorphisms and Derivations on Normed Lie Triple Systems

“…During the last three decades, several stability problems of functional equations have been investigated by a number of mathematicians; compare or confer [8][9][10][11][12] and references therein. Now, we introduce the concept of normed Lie triple systems.…”