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ON FUNCTIONAL INEQUALITIES ASSOCIATED WITH JORDAN-VON NEUMANN TYPE FUNCTIONAL EQUATIONS
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 Title & Authors
ON FUNCTIONAL INEQUALITIES ASSOCIATED WITH JORDAN-VON NEUMANN TYPE FUNCTIONAL EQUATIONS
An, Jong-Su;
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 Abstract
In this paper, it is shown that if f satisfies the following functional inequality (0.1) then f is a bi-additive mapping. We moreover prove that if f satisfies the following functional inequality (0.2) then f is an additive-quadratic mapping.
 Keywords
Jordan-von Neumann type bi-additive functional equation;Jordan-von Neumann type additive-quadratic functional equation;Hyers-Ulam-Rassias stability; functional inequality;
 Language
English
 Cited by
 References
1.
S. Czerwik, On the stability of the quadratic mapping in normed spaces, Abh. Math. Sem. Uni. Hamburg. 27 (1992), 59-64 crossref(new window)

2.
W. Fechner, Stability of a functional inequalities associated with the Jordan-von Neumann functional equation, Aequationes Math. 71 (2006), 149-161 crossref(new window)

3.
A. Gilanyi, Eine zur Parallelogrammgleichung aquivalente Ungleichung, Aequationes Math. 62 (2001), 303-309 crossref(new window)

4.
A. Gilanyi, On a problem by K. Nikodem, Math. Inequal. Appl. 5 (2002), 707-710

5.
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)

6.
K. W. Jun, S. M. Jung, and Y. H. Lee, A generalization of the Hyers-Ulam-Rassias stability of a functional equation of division, J. Korean Math. Soc. 41 (2004), no. 3, 501-511 crossref(new window)

7.
K. W. Jun and H. M. Kim, Remarks on the stability of additive functional equation, Bull. Korean Math. Soc. 38 (2001), no. 4, 679-687

8.
K. W. Jun, On the Hyper-Ulam stability of a generalized quadratic and additive functional equation, Bull. Korean Math. Soc. 42 (2005), no. 1, 133-148 crossref(new window)

9.
J. Kang, C. Lee, and Y. Lee, A note on the Hyers-Ulam-Rassias stability of a quadratic equation, Bull. Korean Math. Soc. 41 (2004), no. 3, 541-557 crossref(new window)

10.
G. H. Kim, On the stability of the generalized G-type functional equations, Commun. Korean Math. Soc. 20 (2005), no. 1, 93-106 crossref(new window)

11.
G. H. Kim, On the stability of functional equations in n-variables and its applications, Commun. Korean Math. Soc. 20 (2005), no. 2, 321-338 crossref(new window)

12.
G. H. Kim and Y. W. Lee, The stability of the generalized form for the Gamma functional equation, Commun. Korean Math. Soc. 15 (2000), no. 1, 45-50

13.
G. H. Kim, Y. W. Lee, and K. S. Ji, Modified Hyers-Ulam-Rassias stability of functional equations with square-symmetric operation, Commun. Korean Math. Soc. 16 (2001), no. 2, 211-223

14.
E. H. Lee, On the solution and stability of the quadratic type functional equations, Commun. Korean Math. Soc. 19 (2004), no. 3, 477-493 crossref(new window)

15.
Y. W. Lee, On the stability of mappings in Banach algebras, Commun. Korean Math. Soc. 18 (2003), no. 2, 235-242 crossref(new window)

16.
Y. W. Lee and B. M. Choi, Stability of a Beta-type functional equation with a restricted domain, Commun. Korean Math. Soc. 19 (2004), no. 4, 701-713 crossref(new window)

17.
Gy. Maksa and P. Volkmann, Characterization of group homomorphisms having values in an inner product space, Publ. Math. Debrecen 56 (2000), 197-200

18.
C. Park, Generalized Hyers-Ulam-Rassias stability of n-sesquilinear-quadratic mappings on Banach modules over C*-algebras, J. Comput. Appl. Math. 180 (2005), 279-291 crossref(new window)

19.
C. Park, Y. Cho, and M. Han, Functional inequalities associated with Jordan-von Neumann type additive functional equations, J. Inequal. Appl. 2007, 41820 (2007), 1-13 crossref(new window)

20.
C. G. Park and W. G. Park, On the stability of the Jensen's equation in a Hilbert module, Bull. Korean Math. Soc. 40 (2003), no. 1, 53-61 crossref(new window)

21.
C. Park and Th. M. Rassias, On a generalized Trif's mapping in Banach modules over a C*-algebra, J. Korean Math. Soc. 43 (2006), no. 2, 323-356 crossref(new window)

22.
K. H. Park and Y. S Jung, The stability of a functional inequality with the fixed point alternative, Commun. Korean Math. Soc. 19 (2004), no. 2, 253-266 crossref(new window)

23.
W. G. Park and J. H. Bae On the stability of involutive A-quadratic mappings, Bull. Korean Math. Soc. 43 (2003), no. 4, 737-745 crossref(new window)

24.
Th. M. Rassias, On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc. 72 (1978), 297-300 crossref(new window)

25.
J. Ratz, On inequalities associated with the Jordan-von Neumann functional equation, Aequationes Math. 66 (2003), 191-200 crossref(new window)

26.
T. Trif, Hyers-Ulam-Rassias stability of a quadratic functional equation, Bull. Korean Math. Soc. 40 (2003), no. 2, 253-267 crossref(new window)

27.
S. M. Ulam, A Collection of the Mathematical Problems, Interscience Publ. New York, 1960