International Journal of Mathematics and Mathematical Sciences
Volume 6 (1983), Issue 3, Pages 419-429
Local expansions and accretive mappings
Department of Mathematics, The University of Iowa, lowa City 52242, lowa, USA
Received 14 February 1983; Revised 24 March 1983
Copyright © 1983 W. A. Kirk. 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.
Let and be complete metric spaces with metrically convex, let be open, fix , and let for all . Let be a closed mapping which maps open subsets of onto open sets in , and suppose is locally expansive on in the sense that there exists a continuous nonincreasing function with such that each point has a neighborhood for which for all . Then, given , it is shown that iff there exists such that for , . This result is then applied to the study of existence of zeros of (set-valued) locally strongly accretive and -accretive mappings in Banach spaces