Communications of the
Korean Mathematical Society CKMS

ISSN(Print) 1225-1763 ISSN(Online) 2234-3024
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Commun. Korean Math. Soc. 2010; 25(3): 405-417

Printed September 1, 2010

https://doi.org/10.4134/CKMS.2010.25.3.405

Copyright © The Korean Mathematical Society.

Fuzzy stability of a generalized quadratic functional equation

Abbas Najati

University of Mohaghegh Ardabili

Abstract

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We prove the generalized Hyers--Ulam stability of the generalized quadratic functional equation \[f(rx+sy)=r^2f(x)+s^2f(y)+\frac{rs}{2}[f(x+y)-f(x-y)]\] in fuzzy Banach spaces, where $r,s$ are non-zero rational numbers with $r^2+s^2\neq1.$

Keywords: stability, fuzzy Banach spaces, quadratic mapping

MSC numbers: Primary 46S40; Secondary 39B52, 39B82, 26E50, 46S50

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