A fixed point approach to almost quartic mappings in quasi fuzzy normed spaces

We will define a notion for a quasi fuzzy p-normed space, then we use the fixed point alternative theorem to establish Hyers–Ulam–Rassias stability of the quartic functional equation where functions map a linear space into a complete quasi fuzzy p-normed space. Later, we will show that there exists...

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Bibliographic Details
Published in:Fuzzy sets and systems 2009-06, Vol.160 (11), p.1653-1662
Main Author: Mirmostafaee, Alireza Kamel
Format: Article
Language:English
Subjects:
Analysis
Applied sciences
Circuit properties
Computer science
control theory
systems
Control theory. Systems
Digital circuits
Electric, optical and optoelectronic circuits
Electronic circuits
Electronics
Exact sciences and technology
Fixed point alternative
Fuzzy normed space
Fuzzy stability
Hyers–Ulam–Rassias stability
Information, signal and communications theory
Mathematical methods
Miscellaneous
Quartic functional equation
System theory
Telecommunications and information theory
Theoretical computing
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Summary:We will define a notion for a quasi fuzzy p-normed space, then we use the fixed point alternative theorem to establish Hyers–Ulam–Rassias stability of the quartic functional equation where functions map a linear space into a complete quasi fuzzy p-normed space. Later, we will show that there exists a close relationship between the fuzzy continuity behavior of a fuzzy almost quartic function, control function and the unique quartic mapping which approximates the almost quartic map. Finally, some applications of our results in the stability of quartic mappings from a linear space into a quasi p-norm space will be exhibited.
ISSN:0165-0114
1872-6801
DOI:10.1016/j.fss.2009.01.011