HYERS-ULAM-RASSIAS STABILITY OF THE APOLLONIUS TYPE QUADRATIC MAPPING IN RN-SPACES
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Authors
H. AZADI KENARY
- Department of Mathematics, College of Science, Yasouj University, Yasouj 75914-353, Iran.
K. SHAFAAT
- Department of Mathematics, College of Science, Yasouj University, Yasouj 75914-353, Iran.
M. SHAFEI
- Department of Mathematics, College of Science, Yasouj University, Yasouj 75914-353, Iran.
G. TAKBIRI
- Department of Mathematics, College of Science, Yasouj University, Yasouj 75914-353, Iran.
Abstract
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.
Share and Cite
ISRP Style
H. AZADI KENARY, K. SHAFAAT, M. SHAFEI, G. TAKBIRI, HYERS-ULAM-RASSIAS STABILITY OF THE APOLLONIUS TYPE QUADRATIC MAPPING IN RN-SPACES, Journal of Nonlinear Sciences and Applications, 4 (2011), no. 1, 82-91
AMA Style
KENARY H. AZADI, SHAFAAT K., SHAFEI M., TAKBIRI G., HYERS-ULAM-RASSIAS STABILITY OF THE APOLLONIUS TYPE QUADRATIC MAPPING IN RN-SPACES. J. Nonlinear Sci. Appl. (2011); 4(1):82-91
Chicago/Turabian Style
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 Applications, 4, no. 1 (2011): 82-91
Keywords
- Fixed point theory
- Stability
- Random normed space.
MSC
References
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