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

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.