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On the Bartle-Graves theorem

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posted on 2025-05-10, 08:16 authored by J. 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.

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