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 $f\left(rx+sy\right)+rsf\left(x-y\right)=\left(r+s\right)\left[rf\left(x\right)+sf\left(y\right)\right]$ in fuzzy Banach spaces, where $r$, $s$ are nonzero rational numbers with $r^2+rs+s^2-1\ne 0$, $r+s\ne 0$.