Geodesic
The Stability of a Generalized Affine Functional Equation in Fuzzy Normed Spaces
Publications de l'Institut Mathématique, _N_S_100 (2016) no. 114, p. 163

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We obtain the general solution of the following functional equation \begin{multline*} f(kx_1+x_2+\cdots+x_k)+f(x_1+kx_2+\cdots+x_k)+\cdots+f(x_1+x_2+\cdots+kx_k) +f(x_1)+f(x_2)+\cdots+f(x_k)=2kf(x_1+x_2+\cdots+x_k),~k\geq2. \end{multline*} 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.
DOI : 10.2298/PIM1614163M
Classification : 39B52, 39B82 26E50
Keywords: functional equation, Hyers--Ulam--Rassias stability, fuzzy normed space, fixed point alternative method 
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M. Mursaleen; Khursheed J. Ansari. The Stability of a Generalized Affine Functional Equation in Fuzzy Normed Spaces. Publications de l'Institut Mathématique, _N_S_100 (2016) no. 114, p. 163 . doi: 10.2298/PIM1614163M

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