JOURNAL BROWSE
Search
Advanced SearchSearch Tips
STABILITY OF AN ADDITIVE FUNCTIONAL INEQUALITY IN PROPER CQ*-ALGEBRAS
facebook(new window)  Pirnt(new window) E-mail(new window) Excel Download
 Title & Authors
STABILITY OF AN ADDITIVE FUNCTIONAL INEQUALITY IN PROPER CQ*-ALGEBRAS
Lee, Jung-Rye; Park, Choon-Kil; Shin, Dong-Yun;
  PDF(new window)
 Abstract
In this paper, we prove the Hyers-Ulam-Rassias stability of the following additive functional inequality: We investigate homomorphisms in proper -algebras and derivations on proper -algebras associated with the additive functional inequality (0.1).
 Keywords
additive functional inequality;Hyers-Ulam-Rassias stability;proper -algebras;proper -algebra homomorphism;derivation;
 Language
English
 Cited by
1.
ON THE STABILITY OF A GENERAL ADDITIVE FUNCTIONAL INEQUALITY IN BANACH SPACES,;

충청수학회지, 2013. vol.26. 4, pp.907-913 crossref(new window)
2.
ON THE HYERS-ULAM STABILITY OF AN ADDITIVE FUNCTIONAL INEQUALITY,;;;

충청수학회지, 2013. vol.26. 4, pp.671-681 crossref(new window)
3.
STABILITY OF AN ADDITIVE FUNCTIONAL INEQUALITY IN BANACH SPACES,;

충청수학회지, 2016. vol.29. 1, pp.103-108 crossref(new window)
1.
STABILITY OF AN ADDITIVE FUNCTIONAL INEQUALITY IN BANACH SPACES, Journal of the Chungcheong Mathematical Society, 2016, 29, 1, 103  crossref(new windwow)
2.
ON THE HYERS-ULAM STABILITY OF AN ADDITIVE FUNCTIONAL INEQUALITY, Journal of the Chungcheong Mathematical Society, 2013, 26, 4, 671  crossref(new windwow)
3.
ON THE STABILITY OF A GENERAL ADDITIVE FUNCTIONAL INEQUALITY IN BANACH SPACES, Journal of the Chungcheong Mathematical Society, 2013, 26, 4, 907  crossref(new windwow)
 References
1.
J. P. Antoine, A. Inoue, and C. Trapani, $O^\ast$-dynamical systems and $\ast$-derivations of unbounded operator algebras, Math. Nachr. 204 (1999), 5-28. crossref(new window)

2.
J. P. Antoine, A. Inoue, and C. Trapani, Partial $\ast$-Algebras and Their Operator Realizations, Kluwer, Dordrecht, 2002.

3.
F. Bagarello, Applications of topological $\ast$-algebras of unbounded operators, J. Math. Phys. 39 (1998), no. 11, 6091-6105. crossref(new window)

4.
F. Bagarello, A. Inoue, and C. Trapani, Some classes of topological quasi $\ast$-algebras, Proc. Amer. Math. Soc. 129 (2001), no. 10, 2973-2980. crossref(new window)

5.
F. Bagarello, A. Inoue, and C. Trapani, Derivations of quasi $\ast$-algebras, Int. J. Math. Math. Sci. 2004 (2004), no. 21-24, 1077-1096. crossref(new window)

6.
F. Bagarello, A. Inoue, and C. Trapani, Exponentiating derivations of quasi $\ast$-algebras: possible approaches and applications, Int. J. Math. Math. Sci. 2005 (2005), no. 17, 2805-2820. crossref(new window)

7.
F. Bagarello and C. Trapani, States and representations of $CQ^\ast$-algebras, Ann. Inst. H. Poincare Phys. Theor. 61 (1994), no. 1, 103-133.

8.
F. Bagarello and C. Trapani, $CQ^\ast$-algebras: structure properties, Publ. Res. Inst. Math. Sci. 32 (1996), no. 1, 85-116. crossref(new window)

9.
S. Czerwik, Functional Equations and Inequalities in Several Variables, World Scientific Publishing Company, New Jersey, London, Singapore and Hong Kong, 2002.

10.
S. Czerwik, Stability of Functional Equations of Ulam-Hyers-Rassias Type, Hadronic Press, Palm Harbor, Florida, 2003.

11.
Z. Gajda, On stability of additive mappings, Int. J. Math. Math. Sci. 14 (1991), no. 3, 431-434. crossref(new window)

12.
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)

13.
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)

14.
D. H. Hyers, G. Isac, and Th. M. Rassias, Stability of Functional Equations in Several Variables, Birkhauser, Basel, 1998.

15.
D. H. Hyers and Th. M. Rassias, Approximate homomorphisms, Aequationes Math. 44 (1992), no. 2-3, 125-153. crossref(new window)

16.
C. Park, Lie $\ast$-homomorphisms between Lie $C^\ast$-algebras and Lie $\ast$-derivations on Lie $C^\ast$-algebras, J. Math. Anal. Appl. 293 (2004), no. 2, 419-434. crossref(new window)

17.
C. Park, Homomorphisms between Lie $JC^\ast$-algebras and Cauchy-Rassias stability of Lie $JC^\ast$-algebra derivations, J. Lie Theory 15 (2005), no. 2, 393-414.

18.
C. Park, Isomorphisms between unital $C^\ast$-algebras, J. Math. Anal. Appl. 307 (2005), no. 2, 753-762. crossref(new window)

19.
C. Park, Approximate homomorphisms on $JB^\ast$-triples, J. Math. Anal. Appl. 306 (2005), no. 1, 375-381. crossref(new window)

20.
C. Park, Isomorphisms between $C^\ast$-ternary algebras, J. Math. Phys. 47 (2006), no. 10, 103512, 12 pp. crossref(new window)

21.
C. Park, Hyers-Ulam-Rassias stability of a generalized Apollonius-Jensen type additive mapping and isomorphisms between $C^\ast$-algebras, Math. Nachr. 281 (2008), no. 3, 402-411. crossref(new window)

22.
J. M. Rassias, On approximation of approximately linear mappings by linear mappings, J. Funct. Anal. 46 (1982), no. 1, 126-130. crossref(new window)

23.
J. M. Rassias, On approximation of approximately linear mappings by linear mappings, Bull. Sci. Math. (2) 108 (1984), no. 4, 445-446.

24.
J. M. Rassias, Solution of a problem of Ulam, J. Approx. Theory 57 (1989), no. 3, 268-273. crossref(new window)

25.
J. 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)

26.
J. M. Rassias, Problem 16; 2, Report of the 27th International Symp. on Functional Equations, Aequationes Math. 39 (1990), 292-293; 309.

27.
J. 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)

28.
J. M. Rassias, On the stability of functional equations in Banach spaces, J. Math. Anal. Appl. 251 (2000), no. 1, 264-284. crossref(new window)

29.
J. 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)

30.
J. M. Rassias, Functional Equations, Inequalities and Applications, Kluwer Academic Publishers, Dordrecht, Boston and London, 2003.

31.
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)

32.
F. Skof, Proprieta localie approssimazione di operatori, Rend. Sem. Mat. Fis. Milano 53 (1983), 113-129. crossref(new window)

33.
C. Trapani, Quasi-$\ast$-algebras of operators and their applications, Rev. Math. Phys. 7 (1995), no. 8, 1303-1332. crossref(new window)

34.
C. Trapani, Some seminorms on quasi-$\ast$-algebras, Studia Math. 158 (2003), no. 2, 99-115. crossref(new window)

35.
C. Trapani, Bounded elements and spectrum in Banach quasi $\ast$-algebras, Studia Math. 172 (2006), no. 3, 249-273. crossref(new window)

36.
S. M. Ulam, Problems in Modern Mathematics, Wiley, New York, 1960.