Abstract

In this paper, we introduce and solve the following quadratic (<TEX>${\rho}_1$</TEX>, <TEX>${\rho}_2$</TEX>)-functional inequality (0.1) <TEX>$$N\left(2f({\frac{x+y}{2}})+2f({\frac{x-y}{2}})-f(x)-f(y),t\right){\leq}min\left(N({\rho}_1(f(x+y)+f(x-y)-2f(x)-2f(y)),t),\;N({\rho}_2(4f(\frac{x+y}{2})+f(x-y)-2f(x)-2f(y)),t)\right)$$</TEX> in fuzzy normed spaces, where <TEX>${\rho}_1</TEX><TEX>$</TEX> and <TEX>${\rho}_2$</TEX> are fixed nonzero real numbers with <TEX>${{\frac{1}{{4\left|{\rho}_1\right|}}+{{\frac{1}{{4\left|{\rho}_2\right|}}$</TEX> < 1, and f(0) = 0. Using the fixed point method, we prove the Hyers-Ulam stability of the quadratic (<TEX>${\rho}_1$</TEX>, <TEX>${\rho}_2$</TEX>)-functional inequality (0.1) in fuzzy Banach spaces.