Fuzzy Stability of Jensen-Type Quadratic Functional Equations

Abstract

We prove the generalized Hyers-Ulam stability of the following quadratic functional equations $2f\left((x+y)/2\right)+2f\left((x-y)/2\right)=f\left(x\right)+f\left(y\right)$ and $f\left(ax+ay\right)+\left(ax-ay\right)=2a^{2}f\left(x\right)+2a^{2}f\left(y\right)$ in fuzzy Banach spaces for a nonzero real number $a$ with $a\ne \pm 1/2$.