JOURNAL BROWSE
Search
Advanced SearchSearch Tips
FUZZY STABILITY OF THE CAUCHY ADDITIVE AND QUADRATIC TYPE FUNCTIONAL EQUATION
facebook(new window)  Pirnt(new window) E-mail(new window) Excel Download
 Title & Authors
FUZZY STABILITY OF THE CAUCHY ADDITIVE AND QUADRATIC TYPE FUNCTIONAL EQUATION
Jin, Sun-Sook; Lee, Yang-Hi;
  PDF(new window)
 Abstract
In this paper, we investigate a fuzzy version of stability for the functional equation in the sense of M. Mirmostafaee and M. S. Moslehian.
 Keywords
fuzzy normed space;fuzzy almost quadratic-additive mapping;Cauchy additive and quadratic type functional equation;
 Language
English
 Cited by
1.
STABILITY OF FUNCTIONAL EQUATION AND INEQUALITY IN FUZZY NORMED SPACES,;;

충청수학회지, 2013. vol.26. 4, pp.707-721 crossref(new window)
1.
STABILITY OF FUNCTIONAL EQUATION AND INEQUALITY IN FUZZY NORMED SPACES, Journal of the Chungcheng Mathematical Society, 2013, 26, 4, 707  crossref(new windwow)
2.
A General Uniqueness Theorem concerning the Stability of Additive and Quadratic Functional Equations, Journal of Function Spaces, 2015, 2015, 1  crossref(new windwow)
 References
1.
T. Aoki, On the stability of the linear transformation in Banach spaces, J. Math. Soc. Japan 2 (1950), 64-66. crossref(new window)

2.
T. Bag and S. K. Samanta, Finite dimensional fuzzy normed linear spaces, J. Fuzzy Math. 11 (2003), no. 3, 687-705.

3.
S. C. Cheng and J. N. Mordeson, Fuzzy linear operator and fuzzy normed linear spaces, Bull. Calcutta Math. Soc. 86 (1994), no. 5, 429-436.

4.
S. Czerwik, On the stability of the quadratic mapping in normed spaces, Abh. Math. Sem. Univ. Hamburg 62 (1992), 59-64. crossref(new window)

5.
P. Gavruta, A generalization of the Hyers-Ulam-Rassias stability of approximately additive mappings, J. Math. Anal. Appl. 184 (1994), no. 3, 431-436. crossref(new window)

6.
D. H. Hyers, On the stability of the linear functional equation, Proc. Natl. Acad. Sci. USA 27 (1941), 222-224. crossref(new window)

7.
K.-W. Jun and Y.-H. Lee, A generalization of the Hyers-Ulam-Rassias stability of the Pexiderized quadratic equations. II, Kyungpook Math. J. 47 (2007), no. 1, 91-103.

8.
A. K. Katsaras, Fuzzy topological vector spaces II, Fuzzy Sets and Systems 12 (1984), no. 2, 143-154. crossref(new window)

9.
G.-H. Kim, On the stability of functional equations with square-symmetric operation, Math. Inequal. Appl. 4 (2001), no. 2, 257-266.

10.
H.-M. Kim, On the stability problem for a mixed type of quartic and quadratic functional equation, J. Math. Anal. Appl. 324 (2006), no. 1, 358-372. crossref(new window)

11.
I. Kramosil and J. Michalek, Fuzzy metric and statistical metric spaces, Kybernetika (Prague) 11 (1975), no. 5, 326-334.

12.
Y.-H. Lee, On the Hyers-Ulam-Rassias stability of the generalized polynomial function of degree 2, J. Chuncheong Math. Soc. 22, (2009) 201-209.

13.
Y.-H. Lee, On the stability of the monomial functional equation, Bull. Korean Math. Soc. 45 (2008), no. 2, 397-403. crossref(new window)

14.
Y. H. Lee and K. W. Jun, A generalization of the Hyers-Ulam-Rassias stability of Jensen's equation, J. Math. Anal. Appl. 238 (1999), no. 1, 305-315. crossref(new window)

15.
Y. H. Lee and K. W. Jun, A generalization of the Hyers-Ulam-Rassias stability of the Pexider equation, J. Math. Anal. Appl. 246 (2000), no. 2, 627-638. crossref(new window)

16.
Y. H. Lee and K. W. Jun, On the stability of approximately additive mappings, Proc. Amer. Math. Soc. 128 (2000), no. 5, 1361-1369. crossref(new window)

17.
A. K. Mirmostafaee and M. S. Moslehian, Fuzzy almost quadratic functions, Results Math. 52 (2008), no. 1-2, 161-177. crossref(new window)

18.
A. K. Mirmostafaee and M. S. Moslehian, Fuzzy versions of Hyers-Ulam-Rassias theorem, Fuzzy Sets and Systems 159 (2008), no. 6, 720-729. crossref(new window)

19.
C.-G. Park, On the stability of the Cauchy additive and quadratic type functional equation, to appear.

20.
Th. M. Rassias, On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc. 72 (1978), no. 2, 297-300. crossref(new window)

21.
F. Skof, Local properties and approximations of operators, Rend. Sem. Mat. Fis. Milano 53 (1983), 113-129. crossref(new window)

22.
S. M. Ulam, A Collection of Mathematical Problems, Interscience, New York, 1968.