Solution and Hyers-Ulam-Rassias Stability of Generalized Mixed Type Additive-Quadratic Functional Equations in Fuzzy Banach Spaces

Abstract

By using fixed point methods and direct method, we establish the generalized Hyers-Ulam stability of the following additive-quadratic functional equation $f\left(x+ky\right)+f\left(x-ky\right)=f\left(x+y\right)+f\left(x-y\right)+$ $\left(2\left(k+1\right)/k\right)f\left(ky\right)-2\left(k+1\right)f\left(y\right)$ for fixed integers $k$ with $k\ne 0,\pm 1$ in fuzzy Banach spaces.