Abstract and Applied Analysis
Volume 4 (1999), Issue 2, Pages 83-100
doi:10.1155/S108533759900010X
A-properness and fixed point theorems for dissipative type maps
1Department of Mathematics and Statistics, York University, 4700 Keele Street, Toronto M3J 1P3, Ontario, Canada
2Department of Mathematics, University of Glasgow, Glasgow G12 8QW, UK
Received 26 April 1999
Copyright © 1999 K. Q. Lan and J. R. L. Webb. 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.
Abstract
We obtain new A-properness results for demicontinuous, dissipative type mappings defined only on closed convex subsets of a Banach space X with uniformly convex dual and which satisfy a property called weakly inward. The method relies on a new property of the duality mapping in such spaces. New fixed point results are obtained by utilising a theory of fixed point index.