Fuzzy almost quadratic functions (Q941111)

The authors approximate a fuzzy almost quadratic function by a quadratic function in a fuzzy sense; this kind of fuzzy normed linear space was introduced by \textit{T. Bag} and \textit{S. K. Samanta} [J. Fuzzy Math. 11, 687--705 (2003; Zbl 1045.46048)]. More precisely, they establish a fuzzy Hyers-Ulam-Rassias stability of the quadratic functional equation \(f(x+y)+f(x-y)=2f(x)+2f(y)\). Their result can be regarded as a generalization of the stability phenomenon in the framework of normed linear spaces. They also prove a generalized version of fuzzy stability of the Pexiderized quadratic functional equation \(f(x+y)+f(x-y)=2g(x)+2h(y)\).