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A Fixed Point Approach to the Stability of a Generalized Quadratic and Additive Functional Equation
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  • Journal title : Kyungpook mathematical journal
  • Volume 53, Issue 2,  2013, pp.219-232
  • Publisher : Department of Mathematics, Kyungpook National University
  • DOI : 10.5666/KMJ.2013.53.2.219
 Title & Authors
A Fixed Point Approach to the Stability of a Generalized Quadratic and Additive Functional Equation
Jin, Sun Sook; Lee, Yang-Hi;
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 Abstract
In this paper, we investigate the stability of the functional equation $$f(x+2y)-2f(x+y)+2f(x-y)-f(x-2y)
 Keywords
generalized quadratic and additive functional equation;fixed point method;Hyers-Ulam-Rassias stability;
 Language
English
 Cited by
 References
1.
T. Aoki, On the stability of the linear transformation in Banach spaces, J. Math. Soc. Japan, 2(1950), 64-66. crossref(new window)

2.
L. Cadariu and V. Radu, Fixed points and the stability of Jensen's functional equation, J. Inequal. Pure Appl. Math., 4(2003), article 4.

3.
L. Cadariu and V. Radu, Fixed points and the stability of quadratic functional equations, An. Univ. Timisoara Ser. Mat.-Inform., 41(2003), 25-48.

4.
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. crossref(new window)

5.
P. Gavruta, A generalization of the Hyers-Ulam-Rassias stability of approximately additive mappings, J. Math. Anal. Appl., 184(1994), 431-436. crossref(new window)

6.
D. H. Hyers, On the stability of the linear functional equation, Proc. Natl. Acad. Sci. USA, 27(1941), 222-224. crossref(new window)

7.
K. -W. Jun and H. -M. Kim, On the Hyers-Ulam stability of a generalized quadratic and additive functional equation, Bull. Korean Math. Soc., 42(2005), 133-148. crossref(new window)

8.
K. -W. Jun and H. -M. Kim, On the stability of a general quadratic functional equation and applications, J. Chungcheong Math. Soc., 17(2004), 57-75.

9.
K. -W. Jun and Y. -H. Lee, A generalization of the Hyers-Ulam-Rassias stability of the Pexiderized quadratic equations, II, Kyungpook Math. J., 47(2007), 91-103.

10.
K. -W. Jun Y. -H. Lee, and J. R. Lee, On the stability of a new Pexider type functional equation, J. Inequal. Appl., 2008, ID 816963, 22pages.

11.
G. -H. Kim, On the stability of functional equations with square-symmetric operation, Math. Inequal. Appl., 4(2001), 257-266.

12.
Y. -H. Lee, On the stability of the monomial functional equation, Bull. Korean Math. Soc., 45(2008), 397-403. crossref(new window)

13.
Y. H. Lee and K. W. Jun, A generalization of the Hyers-Ulam-Rassias stability of Jensen's equation, J. Math. Anal. Appl., 238(1999), 305-315. crossref(new window)

14.
Y. H. Lee and K. W. Jun, A generalization of the Hyers-Ulam-Rassias stability of Pexider equation, J. Math. Anal. Appl., 246(2000), 627-638. crossref(new window)

15.
Y. H. Lee and K. W. Jun, A note on the Hyers-Ulam-Rassias stability of Pexider equation, J. Korean Math. Soc., 37(2000), 111-124.

16.
Y. H. Lee and K. W. Jun, On the stability of approximately additive mappings, Proc. Amer. Math. Soc., 128(2000), 1361-1369. crossref(new window)

17.
Th. M. Rassias, On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc., 72(1978), 297-300. crossref(new window)

18.
I. A. Rus, Principles and applications of fixed point theory, Ed. Dacia, Cluj-Napoca 1979, (in Romanian).

19.
S. M. Ulam, A Collection of Mathematical Problems, Interscience, New York, 1960.