Nonlinear fuzzy approximation of a mixed type ACQ functional equation via fixed point alternative
详细信息    查看全文
  • 作者:Hassan Azadi Kenary (2)
  • 关键词:Hyers ; Ulam stability ; Fuzzy Banach space ; Fixed point method ; 39B52 ; 46S40 ; 34K36 ; 47S40 ; 26E50 ; 47H10 ; 39B82
  • 刊名:Mathematical Sciences
  • 出版年:2012
  • 出版时间:December 2012
  • 年:2012
  • 卷:6
  • 期:1
  • 全文大小:205KB
  • 参考文献:1. Katsaras AK: Fuzzy topological vector spaces. / Fuzzy Sets and Syst 1984, 12:143鈥?54. CrossRef
    2. Felbin C: Finite-dimensional fuzzy normed linear space. / Fuzzy Sets and Syst 1992, 48:239鈥?48. CrossRef
    3. Krishna SV, Sarma KKM: Separation of fuzzy normed linear spaces. / Fuzzy Sets and Syst 1994, 63:207鈥?17. CrossRef
    4. Park C: Fuzzy stability of a functional equation associated with inner product spaces. / Fuzzy Sets and Syst 2009, 160:1632鈥?642. CrossRef
    5. Bag T, Samanta SK: Finite dimensional fuzzy normed linear spaces. / J Fuzzy Mathematics 2003, 11:687鈥?05.
    6. Cheng SC, Mordeson JN: Fuzzy linear operators and fuzzy normed linear spaces. / Bull. Calcutta Math. Soc 1994, 86:429鈥?36.
    7. Karmosil I, Michalek J: Fuzzy metric and statistical metric spaces. / Kybernetica 1975, 11:326鈥?34.
    8. Bag T, Samanta SK: Fuzzy bounded linear operators. / Fuzzy Sets and Syst 2005, 151:513鈥?47. CrossRef
    9. C膬dariu L, Radu V: Fixed points and the stability of Jensen鈥檚 functional equation. / J. Inequal. Pure Appl. Math 2003,4(1):4.
    10. Diaz J, Margolis B: A fixed point theorem of the alternative for contractions on a generalized complete metric space. / Bull. Amer. Math. Soc 1968, 74:305鈥?09. CrossRef
    11. Ulam SM: / Problems in Modern Mathematics. John Wiley and Sons, New York; 1964.
    12. Hyers DH: On the stability of the linear functional equation. / Proc. Natl. Acad. Sci. USA 1941, 27:222鈥?24. CrossRef
    13. Rassias ThM: On the stability of the linear mapping in Banach spaces. / Proc. Amer. Math. Soc 1978, 72:297鈥?00. CrossRef
    14. Skof F: Local properties and approximation of operators. / Rendiconti del Seminario Matematico e Fisico di Milano 1983, 53:113鈥?29. CrossRef
    15. Cholewa PW: Remarks on the stability of functional equations. / Aequationes Mathematicae 1984, 27:76鈥?6. CrossRef
    16. Czerwik S: On the stability of the quadratic mapping in normed spaces. / Abh. Math. Sem. Univ. Hambourg 1992, 62:239鈥?48.
    17. Eshaghi-Gordji M, Kaboli-Gharetapeh S, Park C, Zolfaghri S: Stability of an additive-cubic-quartic functional equation. / Advances in Difference Equations 2009, 2009:395693.
    18. Agarwal RP, Cho YJ, Saadati R, Wang S: Nonlinear L-fuzzy stability of cubic functional equations. / J. Inequal. Appl 2012, 2012:77. CrossRef
    19. Azadi Kenary H: Non-Archimedean stability of Cauchy-Jensen type functional equation. / Int. J. Nonlinear Anal. Appl 2010,1(2):1鈥?0.
    20. Azadi Kenary H: Stability of a Pexiderial functional equation in random normed spaces. / Rend. Del Circolo Math. Di Palermo 2011,60(1):59鈥?8. CrossRef
    21. Azadi Kenary H, Shafaat Kh, Shafei M, Takbiri G: Hyers-Ulam-Rassias stability of the Appollonius quadratic mapping in RN-spaces. / J. Nonlinear Sci. Appl 2011,4(1):110鈥?19.
    22. Eshaghi-Gordji M, Abbaszadeh S, Park C: / J. Inequal. Appl. 2009, 153084.
    23. Eshaghi Gordji M, Khodaei H, Rassias JM: Fixed point methods for the stability of general quadratic functional equation. / Fixed Point Theory 2011,12(1):71鈥?2.
    24. Eshaghi Gordji M, Park C, Savadkouhi MB: The stability of quartic functional equation with the fixed point alternative. / Fixed Point Theory 2010,11(2):265鈥?72.
    25. Eshaghi Gordji M: Stability of a functional equation deriving from quartic and additive functions. / Bull. Korean Math. Soc 2010,47(3):491鈥?02. CrossRef
    26. Eshaghi Gordji M, Ebadian A, Zolfaghari S: Stability of a functional equation deriving from cubic and quartic functions. / Abstract and Appl. Anal 2008, 2008:801904.
    27. Eshaghi Gordji M, Khodaei H: Solution and stability of generalized mixed type cubic, quadratic and additive functional equation in quasi鈥揃anach spaces. / Nonlinear Analysis鈥揟MA 2009, 71:5629鈥?643. CrossRef
    28. G菐vruta P: A generalization of the Hyers-Ulam-Rassias stability of approximately additive mappings. / J. Math. Anal. Appl 1994, 184:431鈥?36. CrossRef
    29. Jun K, Cho Y: Stability of generalized Jensen quadratic functional equations. / J. Chungcheong Math. Soc 2007, 29:515鈥?23.
    30. Jung S: / Hyers-Ulam-Rassias Stability of Functional Equations in Mathematical Analysis. Hadronic Press, Palm Harbor; 2001.
    31. Khodaei H, Eshaghi Gordji M, Kim SS, Cho YJ: Approximation of radical functional equations related to quadratic and quartic mappings. / J. Math. Anal. Appl 2012, 397:284鈥?97. CrossRef
    32. Lee SH, Im SM, Hwang IS: Quartic functional equations. / J. Math. Anal. Appl 2005,307(2):387鈥?94. CrossRef
    33. Mihet D, Radu V: On the stability of the additive Cauchy functional equation in random normed spaces. / J. Math. Anal. Appl 2008, 343:567鈥?72. CrossRef
    34. Park C: On the stability of the linear mapping in Banach modules. / J. Math. Anal. Appl 2002, 275:711鈥?20. CrossRef
    35. Park C: Modefied Trif鈥檚 functional equations in Banach modules over a C鈭?algebra and approximate algebra homomorphism. / J. Math. Anal. Appl 2003, 278:93鈥?08. CrossRef
    36. Park C, Moradlou F: Stability of homomorphisms and derivations on C鈭?ternary rings. / Taiwanese J. Math 2009, 13:1985鈥?999.
    37. Rassias ThM: On the stability of the quadratic functional equation and it鈥檚 application. / Studia Univ. Babes-Bolyai 1998, XLIII:89鈥?24.
    38. Rassias ThM: On the stability of functional equations in Banach spaces. / J. Math. Anal. Appl 2000, 251:264鈥?84. CrossRef
    39. Rassias ThM, 艩emrl P: On the Hyers-Ulam stability of linear mappings. / J. Math. Anal. Appl. 1993, 173:325鈥?38. CrossRef
    40. Saadati R, Park C: Non-Archimedean $\mathcal {L}$鈩?fuzzy normed spaces and stability of functional equations. / Journal Computers & Mathematics with Applications 2010, 60:2488鈥?496. CrossRef
    41. Saadati R, Park JH: On the intuitionistic fuzzy topological spaces. / Chaos, Solitons and Fractals 2006, 27:331鈥?4. CrossRef
    42. Saadati R, Vaezpour M, Cho YJ: / J. Ineq. Appl. 2009, 214530.
    43. Saadati R, Zohdi MM, Vaezpour SM: Nonlinear L-random stability of an ACQ functional equation. / J. Ineq. Appl 2011, 2011:194394. CrossRef
  • 作者单位:Hassan Azadi Kenary (2)

    2. Department of Mathematics, College of Sciences, Yasouj University, Yasouj, 75914-353, Iran
  • ISSN:2251-7456
文摘
Using the fixed point method, we prove the generalized Hyers-Ulam stability of the following additive-cubic-quartic functional equation: in fuzzy Banach spaces.

© 2004-2018 中国地质图书馆版权所有 京ICP备05064691号 京公网安备11010802017129号

地址:北京市海淀区学院路29号 邮编:100083

电话:办公室:(+86 10)66554848;文献借阅、咨询服务、科技查新:66554700