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Iranian Journal of Fuzzy Systems
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Xu, T., Rassias, M., Xin Xu, W. (2012). A FIXED POINT APPROACH TO THE INTUITIONISTIC FUZZY STABILITY OF QUINTIC AND SEXTIC FUNCTIONAL EQUATIONS. Iranian Journal of Fuzzy Systems, 9(5), 21-40. doi: 10.22111/ijfs.2012.102
Tian Zhou Xu; Matina John Rassias; Wan Xin Xu. "A FIXED POINT APPROACH TO THE INTUITIONISTIC FUZZY STABILITY OF QUINTIC AND SEXTIC FUNCTIONAL EQUATIONS". Iranian Journal of Fuzzy Systems, 9, 5, 2012, 21-40. doi: 10.22111/ijfs.2012.102
Xu, T., Rassias, M., Xin Xu, W. (2012). 'A FIXED POINT APPROACH TO THE INTUITIONISTIC FUZZY STABILITY OF QUINTIC AND SEXTIC FUNCTIONAL EQUATIONS', Iranian Journal of Fuzzy Systems, 9(5), pp. 21-40. doi: 10.22111/ijfs.2012.102
Xu, T., Rassias, M., Xin Xu, W. A FIXED POINT APPROACH TO THE INTUITIONISTIC FUZZY STABILITY OF QUINTIC AND SEXTIC FUNCTIONAL EQUATIONS. Iranian Journal of Fuzzy Systems, 2012; 9(5): 21-40. doi: 10.22111/ijfs.2012.102

A FIXED POINT APPROACH TO THE INTUITIONISTIC FUZZY STABILITY OF QUINTIC AND SEXTIC FUNCTIONAL EQUATIONS

Article 4, Volume 9, Issue 5, November and December 2012, Page 21-40  XML PDF (417 K)
Document Type: Research Paper
DOI: 10.22111/ijfs.2012.102
Authors
Tian Zhou Xu1; Matina John Rassias2; Wan Xin Xu3
1School of Mathematics, Beijing Institute of Technology, Beijing 100081, People's Republic of China
2Department of Statistical, University College London, Science 1-19 Torrington Place, London WC1E 7HB, United Kingdom
3Department of Electrical and Computer Engineering, College of En- gineering, University of Kentucky, Lexington 40506, Usa and School of Communica- tion and Information Engineering, University of Electronic Science and Technology of China
Abstract
The fixed point alternative methods are implemented to give
Hyers-Ulam  stability for  the quintic functional equation $ f(x+3y)
- 5f(x+2y) + 10 f(x+y)- 10f(x)+ 5f(x-y) - f(x-2y) = 120f(y)$ and the
sextic functional equation $f(x+3y) - 6f(x+2y) + 15 f(x+y)- 20f(x)+
15f(x-y) - 6f(x-2y)+f(x-3y) = 720f(y)$   in the setting of
intuitionistic fuzzy normed spaces (IFN-spaces).  This method
introduces a metrical context and shows that the stability is
related to some fixed point of a suitable operator. Furthermore, the
interdisciplinary relation among the fuzzy set theory,  the theory
of intuitionistic spaces and the theory of functional equations are
also presented in the paper.
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