## Banach Journal of Mathematical Analysis

### On the Aleksandrov-Rassias problem and the Hyers-Ulam-Rassias stability problem

#### Abstract

Let $X$ and $Y$ be normed linear spaces. A mapping $T:X \rightarrow Y$ is called preserving the distance $r$ if for all $x,y$ of $X$ with $\|x-y\|_X=r$ then $\|T(x)-T(y)\|=r$. In this paper, we provide an overall account of the development of the Aleksandrov problem, the Aleksandrov-Rassias problem for mappings which preserve distances and details for the Hyers-Ulam-Rassias stability problem.

#### Article information

Source
Banach J. Math. Anal., Volume 1, Number 1 (2007), 11-22.

Dates
First available in Project Euclid: 21 April 2009

https://projecteuclid.org/euclid.bjma/1240321551

Digital Object Identifier
doi:10.15352/bjma/1240321551

Mathematical Reviews number (MathSciNet)
MR2350190

Zentralblatt MATH identifier
1130.39027

#### Citation

Tan, Liyun; Xiang, Shuhuang. On the Aleksandrov-Rassias problem and the Hyers-Ulam-Rassias stability problem. Banach J. Math. Anal. 1 (2007), no. 1, 11--22. doi:10.15352/bjma/1240321551. https://projecteuclid.org/euclid.bjma/1240321551

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