Geodesic
HYERS-ULAM-RASSIAS STABILITY OF THE APOLLONIUS TYPE QUADRATIC MAPPING IN RN-SPACES
KENARY, H. AZADI1 ; SHAFAAT, K.1 ; SHAFEI , M. 1 ; TAKBIRI, G.1
1 Department of Mathematics, College of Science, Yasouj University, Yasouj 75914-353, Iran
Journal of nonlinear sciences and its applications, Tome 4 (2011) no. 1, p. 82-91.

Voir la notice de l'article provenant de la source International Scientific Research Publications

Recently, in [5], Najati and Moradlou proved Hyers-Ulam-Rassias stability of the following quadratic mapping of Apollonius type
$Q(z - x) + Q(z - y) =\frac{ 1}{ 2}Q(x - y) + 2Q ( z -\frac{ x + y}{ 2})$
in non-Archimedean space. In this paper we establish Hyers-Ulam-Rassias stability of this functional equation in random normed spaces by direct method and fixed point method. The concept of Hyers-Ulam-Rassias stability originated from Th. M. Rassias stability theorem that appeared in his paper: On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc. 72 (1978), 297-300.
DOI : 10.22436/jnsa.004.01.08
Classification : 39B22, 39B52, 39B82, 46S10
Keywords: Fixed point theory, Stability, Random normed space.

KENARY, H. AZADI 1 ; SHAFAAT, K. 1 ; SHAFEI , M.  1 ; TAKBIRI, G. 1

1 Department of Mathematics, College of Science, Yasouj University, Yasouj 75914-353, Iran 
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KENARY, H. AZADI; SHAFAAT, K.; SHAFEI , M. ; TAKBIRI, G. HYERS-ULAM-RASSIAS STABILITY OF THE APOLLONIUS TYPE QUADRATIC MAPPING IN RN-SPACES. Journal of nonlinear sciences and its applications, Tome 4 (2011) no. 1, p. 82-91. doi : 10.22436/jnsa.004.01.08. http://geodesic.mathdoc.fr/articles/10.22436/jnsa.004.01.08/

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