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

Document Type: Research Paper

Authors

1 School of Mathematics, Beijing Institute of Technology, Beijing 100081, People's Republic of China

2 Department of Statistical, University College London, Science 1-19 Torrington Place, London WC1E 7HB, United Kingdom

3 Department 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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