ON THE STABILITY OF A GENERALIZED CUBIC FUNCTIONAL EQUATION

Koh, Hee-Jeong; Kang, Dong-Seung

doi:10.4134/BKMS.2008.45.4.739

HOME > Journal Browse > About Journal > Journal Vol & Issue > Full Record

ON THE STABILITY OF A GENERALIZED CUBIC FUNCTIONAL EQUATION

Journal title : Bulletin of the Korean Mathematical Society
Volume 45, Issue 4, 2008, pp.739-748
Publisher : The Korean Mathematical Society
DOI : 10.4134/BKMS.2008.45.4.739

Title & Authors

ON THE STABILITY OF A GENERALIZED CUBIC FUNCTIONAL EQUATION
Koh, Hee-Jeong; Kang, Dong-Seung;

Abstract

In this paper, we obtain the general solution of a generalized cubic functional equation, the Hyers-Ulam-Rassias stability, and the stability by using the alternative fixed point for a generalized cubic functional equation $$4f(\sum_{j

Keywords

Hyers-Ulam-Rassias stability;cubic mapping;

Language

English

Cited by

2time(s) in CrossRef

The generalized cubic functional equation and the stability of cubic Jordan $$*$$ ∗ -derivations, ANNALI DELL'UNIVERSITA' DI FERRARA, 2013, 59, 2, 235

Intuitionistic fuzzy stability of the generalized forms of cubic and quartic functional equations, Journal of Intelligent & Fuzzy Systems, 2016, 30, 4, 2309

References

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

H. Y. Chu and D. S. Kang, On the stability of an n-dimensional cubic functional equation, J. Math. Anal. Appl. 325 (2007), no. 1, 595-607

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

J. B. Diaz and B. Margolis, A fixed point theorem of the alternative for contractions on a generalized complete metric space, Bull. Amer. Math. Soc. 74 (1968), 305-309

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

P. Gavrut¸a, A generalization of the Hyers-Ulam-Rassias stability of approximately additive mappings, J. Math. Anal. Appl. 184 (1994), no. 3, 431-436

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

D. H. Hyers, G. Isac, and Th. M. Rassias, Topics in Nonlinear Analysis and Applications, World Scientific Publishing Company, Singapore, New jersey, London, 1997

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

10.

G. Isac and Th. M. Rassias, Stability of $\psi$-additive mappings: applications to nonlinear analysis, Internat. J. Math. Math. Sci. 19 (1996), no. 2, 219-228

11.

K.-W. Jun and H.-M. Kim, The generalized Hyers-Ulam-Rassias stability of a cubic functional equation, J. Math. Anal. Appl. 274 (2002), no. 2, 867-878

12.

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

13.

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

14.

Th. M. Rassias, On the stability of functional equations and a problem of Ulam, Acta Appl. Math. 62 (2000), no. 1, 23-130

15.

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

16.

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

17.

I. A. Rus, Principles and Appications of Fixed Point Theory, Ed. Dacia, Cluj-Napoca, 1979

18.

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

19.

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