Fuzzy almost quadratic functions. (English) Zbl 1157.46048

Mirmostafaee, Alireza Kamel; Moslehian, Mohammad Sal

Result. Math. 52, No. 1-2, 161-177 (2008).

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 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 \(f(x+y)+f(x-y)=2f(x)+2f(y)\). 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 \(f(x+y)+f(x-y)=2g(x)+2h(y)\).

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 for functional equations
26E50	Fuzzy real analysis
46S50	Functional analysis in probabilistic metric linear spaces

Keywords:

fuzzy normed space; quadratic function; fuzzy almost quadratic function; Hyers-Ulam-Rassias stability

Citations:

Zbl 1045.46048