Hyers-Ulam-Rassias Stability of the Apollonius Type Quadratic Mapping in Rn-Spaces

Abstract

Abstract. Recently, in [5], Najati and Moradlou proved Hyers-Ulam-Rassias stability of the following quadratic mapping of Apollonius typeIn 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.

A fixed point approach to the hyers-ulam stability of a functional equation in various normed spaces

“…The stability problems of several functional equations have been extensively investigated by a number of authors, and there are many interesting results concerning this problem (see [8][9][10][11][12]). …”

Stability of a generalized quadratic functional equation in various spaces: a fixed point alternative approach

“…The stability problems of several functional equations have been extensively investigated by a number of authors, and there are many interesting results concerning this problem (see [38][39][40][41][42][43][44][45][46][47][48][49][50][51]). …”

Nonlinear approximation of an ACQ-functional equation in nan-spaces

“…The result of Rassias has provided a lot of influence during the last three decades in the development of a generalization of the Hyers-Ulam stability concept. This new concept is known as generalized Hyers-Ulam stability or Hyers-Ulam-Rassias stability of functional equations (see [4][5][6][7][8]). Furthermore, in 1994, a generalization of the Rassias' theorem was obtained by Găvruta [9] by replacing the bound ε(|| x|| p + ||y|| p ) by a general control function (x, y).…”