AIMS Mathematics, 2020, 5(5): 5055-5062. doi: 10.3934/math.2020324.

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Ulam stability of two fuzzy number-valued functional equations

College of Mathematics and Physics, Suzhou University of Science and Technology, Suzhou, Jiangsu 215009, P. R. China

In this paper, the Ulam stability of two fuzzy number-valued functional equations in Banach spaces is investigated by using the metric defined on a fuzzy number space. Under some suitable conditions, some properties of the solutions for these equations such as existence and uniqueness are discussed.
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Keywords Ulam stability; functional equations; fuzzy number-valued mapping; Banach space

Citation: Zhenyu Jin, Jianrong Wu. Ulam stability of two fuzzy number-valued functional equations. AIMS Mathematics, 2020, 5(5): 5055-5062. doi: 10.3934/math.2020324


  • 1. S. M. Ulam, Problems in Modern Mathematics, Science Editions, Wiley, New York, 1964.
  • 2. T. Aoki, On the stability of the linear transformation in Banach spaces, J. Math. Soc. Jpn., 2 (1950), 64-66.
  • 3. J. Brzdęk, W. Fechner, M. S. Moslehian, et al. Recent developments of the conditional stability of the homomorphism equation, Banach J. Math. Anal., 9 (2015), 278-326.    
  • 4. J. Brzdęk, K. Ciepliński, A fixed point theorem in n-Banach spaces and Ulam stability, J. Math. Anal. Appl., 470 (2019), 632-646.    
  • 5. P. Gavruta, A generalization of the Hyers-Ulam-Rassias stability of approximately additive mappings, J. Math. Anal. Appl., 184 (1994), 431-436.    
  • 6. S. M. Jung, Hyers-Ulam-Rassias stability of functional equations in nonlinear analysis, optimization and its applications, Springer, New York, 48 (2011).
  • 7. M. S. Moslehian, T. M. Rassias, Stability of functional equations in non-Archimedean spaces, Appl. Anal. Discrete Math., 1 (2007), 325-334.    
  • 8. V. Govindan, S. Murthy, Solution and Hyers-Ulam stability of n-dimensional non-quadratic functional equation in fuzzy normed space using direct method, Mater. Today: Proc., 16 (2019), 384-391.
  • 9. T. M. Rassias, On a modified Hyers-Ulam sequence, J. Math. Anal. Appl., 158 (1991), 106-113.    
  • 10. S. M. Jung, D. Popa, T. M. Rassias, On the stability of the linear functional equation in a single variable on complete metric groups, J. Global Optim., 59 (2014), 165-171.    
  • 11. E. Castillo, M. R. Ruiz-Cobo, Functional equations and modelling in science and engineering, Marcel Dekker, New York, 1992.
  • 12. I. K. Chang, G. Han, Fuzzy stability of a class of additive-quadratic functional equations, J. Comp. Anal. Appl., 23 (2017), 1043-1055.
  • 13. E. Gordjim, H. Khodaei, M. Kamyar, Stability of Cauchy-Jensen type functional equation in generalized fuzzy normed spaces, Comput. Math. Appl., 62 (2011), 2950-2960.    
  • 14. A. K. Mirmostafaee, M. Mirzavaziri, M. S. Moslehian, Fuzzy stability of the Jensen functional equation, Fuzzy Sets Syst., 159 (2008), 730-738.    
  • 15. A. K. Mirmostafaee, M. S. Moslehian, Fuzzy versions of Hyers-Ulam-Rassias theorem, Fuzzy Sets Syst., 159 (2008), 720-729.    
  • 16. J. R. Wu, Z. Y. Jin, A note on Ulam stability of some fuzzy number-valued functional equations, Fuzzy Sets Syst., 375 (2019), 191-195.    
  • 17. J. Ban, Ergodic theorems for random compact sets and fuzzy variables in Banach spaces, Fuzzy Sets Syst., 44 (1991), 71-82.    
  • 18. J. R. Wu, X. N. Gen, The pseudo-convergence of measurable functions on set-valued fuzzy measure space, Soft Comput., 22 (2018), 4347-4351.    
  • 19. Y. Wu, J. R. Wu, Lusin's theorem for monotone set-valued measures on topological spaces, Fuzzy sets Syst., 364 (2019), 111-123.    
  • 20. A. Ebadian, I. Nikoufar, T. M. Rassias, et al. Stability of generalized derivations on Hilbert C*-modules associated with a pexiderized Cauchy-Jensen type functional equation, Acta Math. Sci., 32 (2012), 1226-1238.    
  • 21. G. Lu, C. Park, Hyers-Ulam stability of additive set-valued functional equations, Appl. Math. Lett., 24 (2011), 1312-1316.    


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