Fuzzy almost quadratic functions.

*(English)*Zbl 1157.46048The 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 *T. Bag* and *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 $f(x+y)+f(x-y)=2f\left(x\right)+2f\left(y\right)$. 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 $f(x+y)+f(x-y)=2g\left(x\right)+2h\left(y\right)$.

Reviewer: Congxin Wu (Harbin)

##### MSC:

46S40 | Fuzzy functional analysis |

39B52 | Functional equations for functions with more general domains and/or ranges |

39B82 | Stability, separation, extension, and related topics |

26E50 | Fuzzy real analysis |

46S50 | Functional analysis in probabilistic metric linear spaces |