This is an announcement for the paper "A note on the Cheng-Dong-Zhang Theorem and its applications" by Duanxu Dai.

Abstract: In this paper, we first give a short introduction to recent development on the stability of Banach spaces via $\eps$-isometry and then present an application of the Cheng-Dong-Zhang Theorem to the continuous selections of a set valued map via $\eps-$ isometries.

Archive classification: math.FA

Mathematics Subject Classification: 46B04, 46B20, 54C60 (Primary) 26E25, 46A20, 54C65 (Secondary)

Remarks: 7 pages

Submitted from: dduanxu@163.com

The paper may be downloaded from the archive by web browser from URL

http://front.math.ucdavis.edu/1301.3396

or

http://arXiv.org/abs/1301.3396