Abstract.
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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Received: June 27, 2007. Revised: October 23, 2007.
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Mirmostafaee, A.K., Moslehian, M.S. Fuzzy Almost Quadratic Functions. Result. Math. 52, 161–177 (2008). https://doi.org/10.1007/s00025-007-0278-9
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DOI: https://doi.org/10.1007/s00025-007-0278-9