Abstract and Applied Analysis
Volume 2003 (2003), Issue 2, Pages 93-99

A remark on the approximate fixed-point property

Tadeusz Kuczumow1,2

1Instytut Matematyki, Uniwersytet M. Curie–Skłodowskiej(UMCS), Lublin 20-031, Poland
2Instytut Matematyki PWSZ, Chełm 20-120, Poland

Received 30 November 2001

Copyright © 2003 Tadeusz Kuczumow. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We give an example of an unbounded, convex, and closed set C in the Hilbert space l2 with the following two properties: (i) C has the approximate fixed-point property for nonexpansive mappings, (ii) C is not contained in a block for every orthogonal basis in l2.