Stability of a quadratic functional equation in intuitionistic fuzzy normed spaces
Commun. Korean Math. Soc. 2011 Vol. 26, No. 2, 237-251
https://doi.org/10.4134/CKMS.2011.26.2.237
Printed June 1, 2011
Jae-Hyeong Bae and Won-Gil Park
Kyung Hee University, Mokwon University
Abstract : In this paper, we determine some stability results concerning the $2$-dimensional vector variable quadratic functional equation $f(x+y,z+w)+f(x-y,z-w)=2f(x,z)+2f(y,w)$ in intuitionistic fuzzy normed spaces (IFNS). We define the intuitionistic fuzzy continuity of the $2$-dimensional vector variable quadratic mappings and prove that the existence of a solution for any approximately $2$-dimensional vector variable quadratic mapping implies the completeness of IFNS.
Keywords : intuitionistic fuzzy normed space, stability
MSC numbers : Primary 94D05, 39B82
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