Fuzzy Stability of Quadratic-cubic Functional Equations

In this paper, the direct method and the fixed point alternative method are implemented to give Hyers-Uiam-Rassias stability of the functional equation 6f（x＋y）-6f（x-y）＋4f（3y）=3f（x＋2y）-3f（x-2y）＋9f（2y） in fuzzy Banach spaces. We can find the range of approximate solutions obtained using the direct met...

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Bibliographic Details
Published in:Acta mathematica Sinica. English series Vol. 27; no. 11; pp. 2191 - 2204
Main Authors: Wang, Zhi Hua, Zhang, Wan Xiong
Format: Journal Article
Language:English
Published: Heidelberg Institute of Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society 01.11.2011
Springer Nature B.V
Subjects:
Approximation
Banach space
Banach spaces
Banach空间
Fuzzy
Fuzzy logic
Fuzzy set theory
Mathematical analysis
Mathematics
Mathematics and Statistics
Stability
Studies
函数方程
固定点
模糊
直接法
稳定性
39B52
fixed point alternative method
Hyers-Ulam-Rassias stability
26E50
Fuzzy normed space
46S50
46S40
quadratic-cubic functional equation
39B82
ISSN:1439-8516, 1439-7617
Online Access:Get full text
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Summary:In this paper, the direct method and the fixed point alternative method are implemented to give Hyers-Uiam-Rassias stability of the functional equation 6f（x＋y）-6f（x-y）＋4f（3y）=3f（x＋2y）-3f（x-2y）＋9f（2y） in fuzzy Banach spaces. We can find the range of approximate solutions obtained using the direct method are less than those obtained by using the fixed point alternative method for the above and the functional equation.
Bibliography:11-2039/O1
In this paper, the direct method and the fixed point alternative method are implemented to give Hyers-Uiam-Rassias stability of the functional equation 6f（x＋y）-6f（x-y）＋4f（3y）=3f（x＋2y）-3f（x-2y）＋9f（2y） in fuzzy Banach spaces. We can find the range of approximate solutions obtained using the direct method are less than those obtained by using the fixed point alternative method for the above and the functional equation.
Fuzzy normed space, quadratic-cubic functional equation, fixed point alternative method, Hyers-Ulam-Rassias stability
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ISSN:1439-8516
1439-7617
DOI:10.1007/s10114-011-9250-4