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  • P-ISSN1226-0657
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Vol.22 No.3

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FUZZY STABILITY OF AN ADDITIVE-QUADRATIC FUNCTIONAL EQUATION WITH THE FIXED POINT ALTERNATIVE

Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics / Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, (P)1226-0657; (E)2287-6081
2015, v.22 no.3, pp.285-298
https://doi.org/10.7468/jksmeb.2015.22.3.285
SEO, JEONG PIL
LEE, SUNGJIN
SAADATI, REZA
SEO,, J. P. , LEE,, S. , & SAADATI,, R. (2015). FUZZY STABILITY OF AN ADDITIVE-QUADRATIC FUNCTIONAL EQUATION WITH THE FIXED POINT ALTERNATIVE. Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, 22(3), 285-298, https://doi.org/10.7468/jksmeb.2015.22.3.285

Abstract

In <xref>[41]</xref>, Th.M. Rassias proved that the norm defined over a real vector space V is induced by an inner product if and only if for a fixed positive integer l <graphic></graphic> holds for all x<sub>1</sub>, &#x22EF; , x<sub>2l</sub> &#x2208; V . For the above equality, we can define the following functional equation <graphic></graphic> Using the fixed point method, we prove the Hyers-Ulam stability of the functional equation (0.1) in fuzzy Banach spaces.

keywords
fuzzy Banach space, fixed point, functional equation related to inner product space, Hyers-Ulam stability, quadratic mapping, additive mapping.

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