In this article, two minor flaws made in the preceding paper  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
New Orleans, LA 70118, USA
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