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
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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