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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| Vydáno v: | Acta mathematica Sinica. English series Ročník 27; číslo 11; s. 2191 - 2204 |
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| Jazyk: | angličtina |
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Institute of Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society
01.11.2011
Springer Nature B.V |
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| ISSN: | 1439-8516, 1439-7617 |
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| Abstract | 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. |
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| AbstractList | In this paper, the direct method and the fixed point alternative method are implemented to give Hyers-Ulam-Rassias stability of the functional equation ... 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. (ProQuest: ... denotes formulae and non-USASCII text omitted) In this paper, the direct method and the fixed point alternative method are implemented to give Hyers-Ulam-Rassias stability of the functional equation 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. 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. In this paper, the direct method and the fixed point alternative method are implemented to give Hyers-Ulam-Rassias stability of the functional equation 6 f ( x + y ) - 6 f ( x - y ) + 4 f ( 3 y ) = 3 f ( x + 2 y ) - 3 f ( x - 2 y ) + 9 f ( 2 y ) 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. |
| Author | Zhi Hua WANG Wan Xiong ZHANG |
| AuthorAffiliation | Department of Mathematics, Sichuan University, Chengdu 610064, P. R. China School of Science, Hubei University of Technology, Wuhan 430068, P. R. China College of Mathematics and Statistics, Chongqing University, Chongqing 401331, P. R. China |
| Author_xml | – sequence: 1 givenname: Zhi Hua surname: Wang fullname: Wang, Zhi Hua organization: Department of Mathematics, Sichuan University, School of Science, Hubei University of Technology – sequence: 2 givenname: Wan Xiong surname: Zhang fullname: Zhang, Wan Xiong email: cqumatzwx@163.com organization: College of Mathematics and Statistics, Chongqing University |
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| CitedBy_id | crossref_primary_10_1155_2012_628931 crossref_primary_10_1007_s00010_014_0314_2 |
| Cites_doi | 10.1016/j.jmaa.2007.02.009 10.1090/S0002-9939-1978-0507327-1 10.1016/0021-9045(89)90041-5 10.1090/S0002-9904-1968-11933-0 10.2969/jmsj/00210064 10.1016/0165-0114(94)90351-4 10.1016/S0252-9602(08)60006-5 10.1016/j.aml.2007.07.022 10.1006/jmaa.1994.1211 10.1007/BF02941618 10.1016/0165-0114(84)90034-4 10.1016/j.fss.2004.05.004 10.1007/978-1-4612-1790-9 10.1016/j.jmaa.2003.12.034 10.1007/BF01831117 10.1016/j.fss.2007.09.016 10.1016/0022-1236(82)90048-9 10.1007/s00025-007-0278-9 10.1016/j.fss.2008.06.014 10.1006/jmaa.1997.5856 10.1023/B:AMHU.0000003897.39440.d8 10.1073/pnas.27.4.222 10.1155/2007/63239 10.1016/S0165-0114(02)00274-9 10.1016/j.jmaa.2008.01.100 10.1016/j.fss.2007.07.011 10.1016/j.ins.2008.05.032 10.1016/S0022-247X(03)00276-2 10.1016/j.amc.2006.05.020 10.1016/j.bulsci.2006.07.004 10.1016/0165-0114(92)90338-5 |
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| Keywords | 39B52 fixed point alternative method Hyers-Ulam-Rassias stability 26E50 Fuzzy normed space 46S50 46S40 quadratic-cubic functional equation 39B82 |
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| Notes | 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 SourceType-Scholarly Journals-1 ObjectType-Feature-1 content type line 14 ObjectType-Article-1 ObjectType-Feature-2 content type line 23 |
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| Snippet | In this paper, the direct method and the fixed point alternative method are implemented to give Hyers-Uiam-Rassias stability of the functional equation... In this paper, the direct method and the fixed point alternative method are implemented to give Hyers-Ulam-Rassias stability of the functional equation in... In this paper, the direct method and the fixed point alternative method are implemented to give Hyers-Ulam-Rassias stability of the functional equation ... in... In this paper, the direct method and the fixed point alternative method are implemented to give Hyers-Ulam-Rassias stability of the functional equation 6 f ( x... |
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| SubjectTerms | 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 |
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| Title | Fuzzy Stability of Quadratic-cubic Functional Equations |
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