JOURNAL BROWSE
Search
Advanced SearchSearch Tips
HYERS-ULAM STABILITY OF MAPPINGS FROM A RING A INTO AN A-BIMODULE
facebook(new window)  Pirnt(new window) E-mail(new window) Excel Download
 Title & Authors
HYERS-ULAM STABILITY OF MAPPINGS FROM A RING A INTO AN A-BIMODULE
Oubbi, Lahbib;
  PDF(new window)
 Abstract
We deal with the Hyers-Ulam stability problem of linear mappings from a vector space into a Banach one with respect to the following functional equation: $$f\(\frac{-x+y}{3}\)+f\(\frac{x-3z}{3}\)+f\(\frac{3x-y+3z}{3}\)
 Keywords
Hyers-Ulam stability of functional equations;Hyers-Ulam stability of additive mappings;ring homomorphisms;ring derivations;
 Language
English
 Cited by
1.
Hyers–Ulam stability of a functional equation with several parameters, Afrika Matematika, 2016, 27, 7-8, 1199  crossref(new windwow)
 References
1.
GH. Abbaspour and A. Rahmani, Hyers-Ulam-Rassias and Ulam-Gavruta-Rassias stability of generalized quadtratic functional equations, Advances in Applied Mathematical Analysis 4 (2009), no. 1, 31-38.

2.
B. Blackadar, Operator Algebras, Theory of $C^{\ast}$-Algebras and von Neumann Algebras, Encyclopedia of Mathematical Sciences, 122, Springer, 2006.

3.
D. G. Bourgin, Approximately isometric and multiplicative transformations on continuous function rings, Duke Math. J. 16 (1949), 385-397. crossref(new window)

4.
L. Cadariu and V. Radu, On the stability of the Cauchy functional equation: a fixed point approach, Iteration theory (ECIT '02), 43-52, Grazer Math. Ber., 346, Karl-Franzens-Univ. Graz, Graz, 2004.

5.
L. Cadariu and V. Radu, Fixed points and the stability of the Jensen's functional equation, J. Inequal. Pure and Appl. Math. 4 (2003), no. 1, http//jipam.vu/edu.au, 1-7.

6.
M. Eshaghi Gordji, N. Ghobadipour, and C. Park, Jordan *-homomorphisms between unital $C^{\ast}$-algebras, Commun. Korean Math. Soc. 27 (2012), no. 1, 149-158. crossref(new window)

7.
M. Eshaghi Gordji, T. Karimi, and S. Kaboli Gharetapeh, Approximately n-Jordan homomorphisms on Banach algebras, J. Inequal. Appl. 2009 (2009), Article ID 870843, 8 pages.

8.
P. Gavruta, A generalization of the Hyers-Ulam-Rassias stability of approxiately additive mappings, J. Math. Anal. Appl. 184 (1994), 431-436. crossref(new window)

9.
D. H. Hyers, On the stability of the linear functional equation, Proc. Nat. Acad. Sci. U.S.A. 27 (1941), 222-224. crossref(new window)

10.
K. Jun, S. Jung, and Y. Lee, A generalisation of the Hyers-Ulam-Rassias stability of functional equation of Davison, J. Korean Math. Soc. 41 (2004), 501-511. crossref(new window)

11.
K. Jun and H. Kim, Remarks on the stability of additive functional equation, Bull. Korean Math. Soc. 38 (2001), no. 4, 679-687.

12.
K. Jun, H. Kim, and J. M. Rassias, Extended Hyers-Ulam stability for Cauchy-Jensen mapping, J. Difference Equ. Appl. 13 (2007), no. 12, 1139-1153. crossref(new window)

13.
T. Miura, S. E. Takahasi, and G. Hirasawa, Hyers-Ulam-Rassias stability of Jordan homomorphisms on Banach algebras, J. Inequal. Appl. 2005 (2005), no. 4, 435-441.

14.
M. S. Moslehian, Hyers-Ulam-Rassias stability of generalized derivations, Int. J. Math. Math. Sci. 2006 (2006), Article ID 93942, 8 pages.

15.
L. Oubbi, Ulam-Hyers-Rassias stability problem for several kinds of mappings, Afr. Mat. Springer Verlag, 2012; DOI 10.1007/s13370-012-0078-6 (18 pages). crossref(new window)

16.
K. Park and Y. Jung, Stability of a functional equation obtained by combining two functional equations, J. Appl. Math. & Computing 14 (2004), no. 1-2, 415-422.

17.
C. Park and J. M. Rassias, Stability of the Jensen-type functional equation in $C^{\ast}$-algebras: A fixed point approch, Abstr. Appl. Anal. 2009 (2009), Article ID 360432, 17 pages.

18.
T. 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)

19.
T. M. Rassias, On the stability of functional equations and a problem of Ulam, Acta Appl. Math. 62 (2000), no. 1, 23-130. crossref(new window)

20.
S. M. Ulam, Problems in Modern Mathematics, Chapter VI, Science ed. Wiley, New York, 1940.