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arXiv · 0710.0106

Fuzzy almost quadratic functions

A. K. Mirmostafaee·M. S. Moslehian
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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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A. K. Mirmostafaee, M. S. Moslehian. 2007-09-30. Fuzzy almost quadratic functions. https://doi.org/10.1007/s00025-007-0278-9

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