THE STABILITY OF A GENERALIZED AFFINE FUNCTIONAL EQUATION IN FUZZY NORMED SPACES

M. Mursaleen, Khursheed J. Ansari

Abstract: We obtain the general solution of the following functional equation $$\begin{array}{}\end{array}$$

f(kx1+x2++xk)+f(x1+kx2++xk)++f(x1+x2++kxk)

+f(x1)+f(x2)++f(xk)=2kf(x1+x2++xk), k2. 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.

Keywords: functional equation; Hyers–Ulam–Rassias stability; fuzzy normed space; fixed point alternative method

Classification (MSC2000): 39B52; 39B82; 26E50

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