HYERS-ULAM-RASSIAS STABILITY OF THE APOLLONIUS TYPE QUADRATIC MAPPING IN RN-SPACES

Volume 4, Issue 1, pp 82-91 http://dx.doi.org/10.22436/jnsa.004.01.08

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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.

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Keywords

• Fixed point theory
• Stability
• Random normed space.

MSC

•  39B22
•  39B52
•  39B82
•  46S10

References

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