JOURNAL BROWSE
Search
Advanced SearchSearch Tips
APPROXIMATELY QUINTIC MAPPINGS IN NON-ARCHIMEDEAN 2-NORMED SPACES BY FIXED POINT THEOREM
facebook(new window)  Pirnt(new window) E-mail(new window) Excel Download
 Title & Authors
APPROXIMATELY QUINTIC MAPPINGS IN NON-ARCHIMEDEAN 2-NORMED SPACES BY FIXED POINT THEOREM
KIM, CHANG IL; JUNG, KAP HUN;
 
 Abstract
In this paper, using the fixed point method, we investigate the generalized Hyers-Ulam stability of the system of quintic functional equation $f(x_1+x_2,y)+f(x_1-x_2,y)
 Keywords
quintic functional equation;Hyers-Ulam stability;non-Archimedean 2-normed spaces;fixed point method;
 Language
English
 Cited by
 References
1.
L. Cädariu and V. Radu, Fixed points and the stability of Jensen's functional equation, J. Inequal. Pure Appl. Math., 4 Article ID 4 (2003).

2.
L. Cädariu and V. Radu, On the stability of the Cauchy functional equation: a fixed point approach, Grazer Math. Ber., 346 (2004), 43-52.

3.
S. Czerwik, Functional equations and Inequalities in several variables, World Scientific. New Jersey, London, 2002.

4.
J.B. Diaz and Beatriz Margolis, A fixed points theorem of the alternative, for contractions on a generalized complete metric space, Bull. Amer. Math. Soc., 74 (1968), 305-309. crossref(new window)

5.
G.L. Forti, Hyers-Ulam stability of functional equations in several variables, Aequationes Math., 50 (1995), 143-190. crossref(new window)

6.
S. Gähler, 2-metrische Räumen und ihr topologische structure, Math. Nachr., 26 (1963), 115-148. crossref(new window)

7.
S. Gähler, Linear 2-normierte Räumen, Math. Nachr., 28 (1964), 1-43. crossref(new window)

8.
D.H. Hyers, On the stability of linear functional equation, Proc. Nat. Acad. Sci., 27 (1941), 222-224. crossref(new window)

9.
D.H. Hyers and T.M. Rassias, Approximate homomorphisms, Aequationes Math., 44 (1992), 125-153. crossref(new window)

10.
D.H. Hyers, G. Isac, and T.M. Rassias, Stability of functional equations in several vari-ables, Birkhäuser, Basel, 1998.

11.
M. Janfada and R. Shourvarzi, On solutions and stability of a generalized quadratic on non-Archimedean normed spaces, J. Appl. Math. and Informatics, 30 (2012), 829-845.

12.
K.W. Jun and H.M. Kim, The generalized Hyers-Ulam-Rassias stability of a cubic func-tional equation, J. Math. Anal. Appl., 274 (2002), 867-878. crossref(new window)

13.
S.M. Jung, On the Hyers-Ulam stability of the functional equation that have the quadratic property, J. Math. Anal. Appl., 222 (1998), 126-137. crossref(new window)

14.
C.I. Kim and K.H. Jung, Stability of a cubic functional equation in 2-normed spaces, J. Appl. Math. and Informatics, 32 (2014), No. 5-6, 817-825. crossref(new window)

15.
Z. Lewandowska, Ggeneralized 2-normed spaces, Stuspske Prace Matematyczno-Fizyczne, 1 (2001), 33-40.

16.
Z. Lewandowska, On 2-normed sets, Glasnik Mat. Ser. III, 42 (58) (2003), 99-110. crossref(new window)

17.
A. Najati and F. Moradlou, Stability of a mixed quadratic and additive functional equation in quasi-Banach spaces, J. Appl. Math. and Informatics, 27 (2009), No. 5-6, 1177-1194.

18.
W.G. Park, Approximate additive mapping in 2-Banach spaces and related topics, J. Math. Anal. Appl., 376 (2011), 193-202. crossref(new window)

19.
V. Radu, The fixed point alternative and the stability of functional equations, Fixed Point Theory, 4 (2003), 91-96.

20.
J.M. Rassias, Solution of the Ulam stability problem for cubic mappings, Glasnik Matematički., 36 (56) (2001), 63-72.

21.
F. Skof, Approssimazione di funzioni δ-quadratic su dominio restretto, Atti. Accad. Sci. Torino Cl. Sci. Fis. Mat. Natur., 118 (1984), 58-70.

22.
S.M. Ulam, A Collection of Mathematical Problems, Interscience Tracts in Pure and Applied Mathematics, No. 8, Interscience, New York, NY, USA, 1960.

23.
A. White, 2-Banach spaces, Math. Nachr., 42 (1969), 43-60. crossref(new window)