Abstract
We obtain the general solution of the following functional equation
f (kx(1) + x(2) + ... + x(k))+ f (x(1)+ kx(2) + ... + xk) + ... + f(x(1)+ x(2) + ... + kx(k)) + f(x(1)) + f(x(2)) + ... + f(x(k)) = 2kf (x(1) + x(2) + ... + x(k)), k >= 2.
We establish the Hyers-Ulam-Rassias stability of the above functional equation in the fuzzy normed spaces. More precisely, we show under suitable conditions that a fuzzy q-almost affine mapping can be approximated by an affine mapping. Further, we determine the stability of same functional equation by using fixed point alternative method in fuzzy normed spaces.