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ON A GENERALIZED TRIF'S MAPPING IN BANACH MODULES OVER A C*-ALGEBRA
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 Title & Authors
ON A GENERALIZED TRIF'S MAPPING IN BANACH MODULES OVER A C*-ALGEBRA
Park, Chun-Gil; Rassias Themistocles M.;
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 Abstract
Let X and Y be vector spaces. It is shown that a mapping satisfies the functional equation $(\ddagger)\;+mn_{mn-2}C_{k-1}\;\sum\limits_{i=1}^n\;f(\frac {x_{mi-m+1}+...+x_{mi}} {m}) =k\;{\sum\limits_{1{\leq}i_1<... is additive, and we prove the Cauchy-Rassias stability of the functional equation in Banach modules over a unital . Let A and B be unital or Lie . As an application, we show that every almost homomorphism h : of A into B is a homomorphism when for all unitaries , and d = 0,1,2,..., and that every almost linear almost multiplicative mapping is a homomorphism when h(2x)=2h(x) for all . Moreover, we prove the Cauchy-Rassias stability of homomorphisms in or in Lie , and of Lie derivations in Lie .
 Keywords
Trif's functional equation;Cauchy-Rassias stability;;Lie homomorphism;Lie derivation;
 Language
English
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 References
1.
Z. Gajda, On stability of additive mappings, Internat. J. Math. Math. Sci. 14 (1991), 431-434 crossref(new window)

2.
P. Gavruta, A generalization of the Hyers-Ulam-Rassias stability of approxi- mately additive mappings, J. Math. Anal. Appl. 184 (1994), no. 3, 431-436 crossref(new window)

3.
D. H. Hyers, On the stability of the linear functional equation, Proc. Nat. Acad. Sci. U.S.A. 27 (1941), 222-224

4.
D. H. Hyers and Th. M. Rassias, Approximate homomorphisms, Aequationes Math. 44 (1992), no. 2-3, 125-153 crossref(new window)

5.
K. W. Jun and Y. H. Lee, 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)

6.
R. V. Kadison and G. K. Pedersen, Means and convex combinations of unitary operators, Math. Scand. 57 (1985), no. 2, 249-266

7.
R. V. Kadison and J. R. Ringrose, Fundamentals of the Theory of Operator Algebras, Elementary Theory, Academic Press, New York, 1983

8.
C. Park, On the stability of the linear mapping in Banach modules, J. Math. Anal. Appl. 275 (2002), no. 2, 711-720 crossref(new window)

9.
C. -G. Park and J. Hou, Homomorphisms between C*-algebras associated with the Trif functional equation and linear derivations on C*-algebras, J. Korean Math. Soc. 41 (2004), no. 4, 461-477 crossref(new window)

10.
C. -G. Park and W. -G. Park, On the Jensen's equation in Banach modules, Taiwanese J. Math. 6 (2002), no. 4, 523-531

11.
Th. M. Rassias, On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc. 72 (1978), no. 2, 297-300

12.
Th. M. Rassias, Problem 16; 2, Report of the 27th International Symp. on Functional Equations, Aeq. Math. 39 (1990), 292-293; 309

13.
Th. 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)

14.
Th. M. Rassias, The problem of S.M. Ulam for approximately multiplicative mappings, J. Math. Anal. Appl. 246 (2000), no. 2, 352-378 crossref(new window)

15.
Th. M. Rassias, On the stability of functional equations in Banach spaces, J. Math. Anal. Appl. 251 (2000), no. 1, 264-284 crossref(new window)

16.
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

17.
Th. M. Rassias and P. Semrl, On the Hyers-Ulam stability of linear mappings, J. Math. Anal. Appl. 173 (1993), no. 2, 325-338 crossref(new window)

18.
T. Trif, On the stability of a functional equation deriving from an inequality of Popoviciu for convex functions, J. Math. Anal. Appl. 272 (2002), no. 2, 604-616 crossref(new window)

19.
S. M. Ulam, Problems in Modern Mathematics, Wiley, New York, 1960

20.
H. Upmeier, Jordan algebras in analysis, operator theory, and quantum me- chanics, CBMS Regional Conference Series in Mathematics, 67, Amer. Math. Soc., Providence, 1987