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HYERS-ULAM-RASSIAS STABILITY OF A CUBIC FUNCTIONAL EQUATION
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 Title & Authors
HYERS-ULAM-RASSIAS STABILITY OF A CUBIC FUNCTIONAL EQUATION
Najati, Abbas;
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 Abstract
In this paper, we will find out the general solution and investigate the generalized Hyers-Ulam-Rassias stability problem for the following cubic functional equation 3f(x+3y)+f(3x-y)
 Keywords
hyers-Ulam-Rassias stability;cubic functional equation;
 Language
English
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 References
1.
J. Aczel and J. Dhombres, Functional equations in several variables, Cambridge University Press, Cambridge, 1989

2.
D. Amir, Characterizations of inner product spaces, Birkhauser Verlag, Basel, 1986

3.
C. Baak, Cauchy-Rassias stability of Cauchy-Jensen additive mappings in Banach spaces, Acta Math. Sin. (Engl. Ser.) 22 (2006), no. 6, 1789-1796 crossref(new window)

4.
J. Baker, The stability of the cosine equation, Proc. Amer. Math. Soc. 80 (1980), no. 3, 411-416 crossref(new window)

5.
Y. Benyamini and J. Lindenstrauss, Geometric nonlinear functional analysis. Vol. 1, American Mathematical Society Colloquium Publications, 48. American Mathematical Society, Providence, RI, 2000

6.
P. W. Cholewa, Remarks on the stability of functional equations, Aequationes Math. 27 (1984), no. 1-2, 76-86 crossref(new window)

7.
S. Czerwik, On the stability of the quadratic mapping in normed spaces, Abh. Math. Sem. Univ. Hamburg 62 (1992), 59-64 crossref(new window)

8.
P. Gavruta, A generalization of the Hyers-Ulam-Rassias stability of approximately ad- ditive mappings, J. Math. Anal. Appl. 184 (1994), no. 3, 431-436 crossref(new window)

9.
A. Grabiec, The generalized Hyers-Ulam stability of a class of functional equations, Publ. Math. Debrecen 48 (1996), no. 3-4, 217-235

10.
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)

11.
D. H. Hyers, G. Isac, and Th. M. Rassias, Stability of functional equations in sev- eral variables, Progress in Nonlinear Differential Equations and their Applications, 34, Birkhauser, Basel, 1998

12.
D. H. Hyers, G. Isac, and Th. M. Rassias, On the asymptoticity aspect of Hyers-Ulam stability of mappings, Proc. Amer. Math. Soc. 126 (1998), no. 2, 425-430 crossref(new window)

13.
D. H. Hyers and Th. M. Rassias, Approximate homomorphisms, Aequationes Math. 44 (1992), no. 2-3, 125-153 crossref(new window)

14.
P. Jordan and J. von Neumann, On inner products in linear, metric spaces, Ann. of Math. (2) 36 (1935), no. 3, 719-723 crossref(new window)

15.
K. Jun and H. Kim, Remarks on the stability of additive functional equation, Bull. Korean Math. Soc. 38 (2001), no. 4, 679-687

16.
K. Jun and H. Kim, The generalized Hyers-Ulam-Rassias stability of a cubic functional equation, J. Math. Anal. Appl. 274 (2002), no. 2, 267-278 crossref(new window)

17.
K. Jun and H. Kim, Stability problem for Jensen-type functional equations of cubic mappings, Acta Math. Sin. (Engl. Ser.) 22 (2006), no. 6, 1781-1788 crossref(new window)

18.
K. Jun and Y. Lee, On the Hyers-Ulam-Rassias stability of a Pexiderized quadratic inequality, Math. Inequal. Appl. 4 (2001), no. 1, 93-118

19.
S.-M. Jung, On the Hyers-Ulam stability of the functional equations that have the qua- dratic property, J. Math. Anal. Appl. 222 (1998), no. 1, 126-137 crossref(new window)

20.
S.-M. Jung, On the Hyers-Ulam-Rassias stability of a quadratic functional equation, J. Math. Anal. Appl. 232 (1999), no. 2, 384-393 crossref(new window)

21.
S.-M. Jung, Stability of the quadratic equation of Pexider type, Abh. Math. Sem. Univ. Hamburg 70 (2000), 175-190 crossref(new window)

22.
P. Kannappan, Quadratic functional equation and inner product spaces, Results Math. 27 (1995), no. 3-4, 368-372 crossref(new window)

23.
A. Najati and C. Park, On the Stability of a Cubic Functional Equation, to appear in the Acta Math. Sinica (English Series)

24.
C. Park, Universal Jensen's equations in Banach modules over a $C^*$-algebra and its unitary group, Acta Math. Sin. (Engl. Ser.) 20 (2004), no. 6, 1047-1056 crossref(new window)

25.
C. Park, J. Hou, and S. Oh, Homomorphisms between $JC^*$-algebras and Lie $C^*$-algebras, Acta Math. Sin. (Engl. Ser.) 21 (2005), no. 6, 1391-1398 crossref(new window)

26.
C. Park and Th. M. Rassias, The N-isometric isomorphisms in linear N-normed $C^*$- algebras, Acta Math. Sin. (Engl. Ser.) 22 (2006), no. 6, 1863-1890 crossref(new window)

27.
K.-H. Park and Y.-S. Jung, Stability of a cubic functional equation on groups, Bull. Korean Math. Soc. 41 (2004), no. 2, 347-357 crossref(new window)

28.
Th. 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)

29.
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)

30.
S. Rolewicz, Metric linear spaces, Second edition. PWN-Polish Scientific Publishers, Warsaw; D. Reidel Publishing Co., Dordrecht, 1984

31.
P. K. Sahoo, A generalized cubic functional equation, Acta Math. Sin. (Engl. Ser.) 21 (2005), no. 5, 1159-1166 crossref(new window)

32.
F. Skof, Local properties and approximation of operators, Rend. Sem. Mat. Fis. Milano 53 (1983), 113-129 crossref(new window)

33.
S. M. Ulam, A collection of mathematical problems, Interscience Tracts in Pure and Applied Mathematics, no. 8 Interscience Publishers, New York-London, 1960