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Refined Stability Results of Functional Equation in Four Variables
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  • Journal title : Kyungpook mathematical journal
  • Volume 55, Issue 1,  2015, pp.73-81
  • Publisher : Department of Mathematics, Kyungpook National University
  • DOI : 10.5666/KMJ.2015.55.1.73
 Title & Authors
Refined Stability Results of Functional Equation in Four Variables
Kim, Hark-Mahn; Lee, Soon;
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 Abstract
In this paper, we present the general solution of the functional equation $$rf(\frac{x+y+z+w}{s})+rf(\frac{x+y-z-w}{s})+rf(\frac{x-y+z-w}{s})+rf(\frac{x-y-z+w}{s})
 Keywords
quadratic functional equation;Hyers-Ulam 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.
D. G. Bourgin, Classes of transformations and bordering transformations, Bull. Amer. Math. Soc., 57(1951), 223-237. crossref(new window)

3.
P. W. Cholewa, Remarks on the shability of functional equations, Aequationes Math., 27(1984), 76-86. crossref(new window)

4.
S. Czerwik, On the stability of the quadratic mapping in normed spaces, Abh. Math. Sem. Univ. Hamburg, 62(1992), 59-64. 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. U.S.A., 27(1941), 222-224. crossref(new window)

7.
S. Lee and K. Jun,Hyers-Ulam-Rassias stability of a quadratic type functional equation, Bull. Korean Math. Soc., 40(2003), 183-193. crossref(new window)

8.
S. Lee and C. Park, Hyers-Ulam-Rassias stability of a functional equation in three variables, J. Chungcheong Math. Soc., 16(2)(2003), 11-21.

9.
C. Park, Hyers-Ulam-Rassias stability of an even functional equation in four variables, Kyungpook Math J., 44(2)(2004), 299-304.

10.
Th. M. Rassias, On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc., 72(1978), 297-300. crossref(new window)

11.
F. Skof, Proprieta locali e approssimazione di operatori, Rend. Sem. Mat. Fis. Milano, 53(1983), 113-129. crossref(new window)

12.
S. M. Ulam, A Collection of the Mathematical Problems, Interscience Publ. New York, 1960.