Fuzzy almost quadratic functions

Details Fuzzy almost quadratic functions Fuzzy almost quadratic functions

2007-09-30

arxiv.org/abs/0710.0106v1

Results in Math. 52 (2008), 161--177

Mathematics

Functional Analysis

17 pages

Scientific paper

We approximate a fuzzy almost quadratic function by a quadratic function in a fuzzy sense. More precisely, we establish a fuzzy Hyers--Ulam--Rassias stability of the quadratic functional equation $f(x+y)+f(x-y)=2f(x)+2f(y)$. Our result can be regarded as a generalization of the stability phenomenon in the framework of normed spaces. We also prove a generalized version of fuzzy stability of the Pexiderized quadratic functional equation $f(x+y)+f(x-y)=2g(x)+2h(y)$.

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