JOURNAL BROWSE
Search
Advanced SearchSearch Tips
THE STABILITY OF FUNCTIONAL INEQUALITIES WITH ADDITIVE MAPPINGS
facebook(new window)  Pirnt(new window) E-mail(new window) Excel Download
 Title & Authors
THE STABILITY OF FUNCTIONAL INEQUALITIES WITH ADDITIVE MAPPINGS
Cho, Young-Sun; Jun, Kil-Woung;
  PDF(new window)
 Abstract
In this paper, we prove the generalized Hyers-Ulam stability of the functional inequalities associated with additive functional mappings. Also, we find the solution of these inequalities which satisfy certain conditions.
 Keywords
Jordan-Von Neumann functional equation;generalized Hyers-Ulam stability;functional inequality;
 Language
English
 Cited by
 References
1.
S. Czerwik, Functional Equations and Inequalities in Several Variables, World Scientific Publishing Company, New Jersey, Hong Kong, Singapore and London, 2002.

2.
W. Fechner, Stability of a functional inequalities associated with the Jordan-Von Neumann functional equation, Aequationes Math. 71 (2006), no. 1-2, 149-161. crossref(new window)

3.
Z. Gajda, On stability of additive mappings, Internat. J. Math. Math. Sci. 14 (1991), no. 3, 431-434. crossref(new window)

4.
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)

5.
A. Gilanyi, Eine zur Parallelogrammgleichung aquivalente Ungleichung, Aequationes Math. 62 (2001), no. 3, 303-309. crossref(new window)

6.
A. Gilanyi, On a problem by K. Nikodem, Math. Inequal. Appl. 5 (2002), no. 4, 707-710.

7.
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)

8.
D. H. Hyers, G. Isac, and Th. M. Rassias, Stability of Functional Equations in Several Variables, Birkhauser, Basel, 1998.

9.
K. Jun and Y. Lee, A generalization of the Hyers-Ulam-Rassias stability of the Pexiderized quadratic equations, J. Math. Anal. Appl. 297 (2004), no. 1, 70-86. crossref(new window)

10.
S. Jung, Hyers-Ulam-Rassias Stability of Functional Equations in Mathematical Analysis, Hadronic Press lnc., Palm Harbor, Florida, 2001.

11.
C. Park, Homomorphisms between Poisson $JC^{\ast}$-algebras, Bull. Braz. Math. Soc. (N.S.) 36 (2005), no. 1, 79-97. crossref(new window)

12.
C. Park, Y. Cho, and M. Han, Functional inequality associted with Jordan-Von Neumann type additive functional equation, J. Inequal. Appl. 12 (2007), 1-12. crossref(new window)

13.
C. Park and J. Cui, Generalized stability of $C^{\ast}$-ternary quadratic mappings, Abstract and Applied Analysis Vol. 2007, Article ID 23282, 6 pages, doi:10.1155/2007/23282. crossref(new window)

14.
C. Park and A. Najati, Homomorphisms and derivations in $C^{\ast}$-algebras, Abstract and Applied Analysis (to appear).

15.
J. M. Rassias, On approximation of approximately linear mappings by linear mappings, J. Funct. Anal. 46 (1982), no. 1, 126-130. crossref(new window)

16.
Th. M. Rassias, On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc. 72 (1978), no. 2, 297-300.

17.
Th. M. Rassias, Problem 16; 2, Report of the 27th International Symp. on Functional Equations, Aequationes Math. 39 (1990), 292-293; 309.

18.
Th. M. Rassias and P. Semrl, On the behavior of mappings which do not satisfy Hyers- Ulam stability, Proc. Amer. Math. Soc. 114 (1992), no. 4, 989-993.

19.
J. Ratz, On inequalities associated with the Jordan-Von Neumann functional equation, Aequationes Math. 66 (2003), no. 1-2, 191-200. crossref(new window)

20.
S. M. Ulam, A Collection of the Mathematical Problems, Interscience Publ. New York, 1960.