Abstract and Applied Analysis
Volume 2003 (2003), Issue 2, Pages 111-119

Measure of nonhyperconvexity and fixed-point theorems

Dariusz Bugajewski1 and Rafael Espínola2

1Faculty of Mathematics and Computer Science, Adam Mickiewicz University, Matejki 48/49, Poznań 60-769, Poland
2Departmento de Análisis Matemático, Facultad de Matematicas, Universidad de Sevilla, P.O. Box 1160, Sevilla 41080, Spain

Received 6 November 2001

Copyright © 2003 Dariusz Bugajewski and Rafael Espínola. 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.


The aim of this paper is to work with the measure of nonhyperconvexity in a similar way as J. Cano (1990) does with the index of nonconvexity. We apply this measure to obtain different extensions of the famous Schauder fixed-point theorem in hyperconvex spaces.