Department of Mathematics
Tulane University
New Orleans, LA 70118, USA
email: txiang@tulane.edu
Tian Xiang
Abstract:
In this article, two minor flaws made in the preceding paper [19]
are corrected. And then several remarks concerning expansive mappings and
their connection with monotone operators are observed.
These observations are then used for generalizing the Minty-Browder theorem
[9,2] and further answer to Nirenberg's open question.
Along this lines, a strengthened Nirenberg's problem is formulated and
a surjective result for expansive mappings is obtained.
Finally, two interesting conjectures concerning ``reverse" Schauder
fixed point theorem are raised.
Submitted May 22, 2012. Published January 7, 2013.
Math Subject Classifications: 58C05, 47H05, 47H10.
Key Words: Expansive mapping; fixed point; Monotone operator;
Nirenberg's problem.
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Tian Xiang Department of Mathematics Tulane University New Orleans, LA 70118, USA email: txiang@tulane.edu |
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