posted on 2025-05-10, 08:16authored byJ. M. Borwein, A. L. Dontchev
The Bartle-Graves theorem extends the Banach open mapping principle to a family of linear and bounded mappings, thus showing that surjectivity of each member of the family is equivalent to the openness of the whole family. In this paper we place this theorem in the perspective of recent concepts and results, and present a general Bartle-Graves theorem for set-valued mappings. As applications, we obtain versions of this theorem for mappings defined by systems of inequalities, and for monotone variational inequalities.
History
Journal title
Proceedings of the American Mathematical Society
Volume
131
Pagination
2553-2560
Publisher
American Mathematical Society (AMS)
Language
en, English
College/Research Centre
Faculty of Science and Information Technology
School
School of Mathematical and Physical Sciences
Rights statement
First published in Proceedings of the American Mathematical Society in Vol.131, No.8, pp.2253-2560, 2003 published by the American Mathematical Society.