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Zbl 1157.46048
Mirmostafaee, Alireza Kamel; Moslehian, Mohammad Sal
Fuzzy almost quadratic functions. (English)
[J] Result. Math. 52, No. 1-2, 161-177 (2008). ISSN 1422-6383; ISSN 0378-6218/e

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 {\it T. Bag} and {\it S. K. Samanta} [J. Fuzzy Math. 11, 687--705 (2003; Zbl 1045.46048)].\par 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 $f(x+y)+f(x-y)=2g(x)+2h(y)$.
[Congxin Wu (Harbin)]

MSC 2000:: *46S40 Fuzzy functional analysis
39B52 Functional equations for functions with more general domains
39B82 Stability, separation, extension, and related topics
26E50 Fuzzy real analysis
46S50 Functional analysis in probabilistic metric spaces

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

Citations: Zbl 1045.46048

Cited in: Zbl 1206.46065 Zbl 1201.46062

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