Notes on expansive mappings and a partial answer to Nirenberg's problem

Notes on expansive mappings and a partial answer to Nirenberg's problem

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...

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Bibliographic Details
Main Author: Tian Xiang
Format: Article
Language:English
Published: Texas State University 2013-01-01
Series:Electronic Journal of Differential Equations
Subjects:
Expansive mapping
fixed point
Monotone operator
Nirenberg's problem
Online Access:http://ejde.math.txstate.edu/Volumes/2013/02/abstr.html
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spelling doaj-95ff4cbc2ffd4bc28499787a7c156fa42020-11-24T21:04:36ZengTexas State UniversityElectronic Journal of Differential Equations1072-66912013-01-01201302,116Notes on expansive mappings and a partial answer to Nirenberg's problemTian XiangIn 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. http://ejde.math.txstate.edu/Volumes/2013/02/abstr.htmlExpansive mappingfixed pointMonotone operatorNirenberg's problem
collection DOAJ
language English
format Article
sources DOAJ
author Tian Xiang
spellingShingle Tian Xiang
Notes on expansive mappings and a partial answer to Nirenberg's problem
Electronic Journal of Differential Equations
Expansive mapping
fixed point
Monotone operator
Nirenberg's problem
author_facet Tian Xiang
author_sort Tian Xiang
title Notes on expansive mappings and a partial answer to Nirenberg's problem
title_short Notes on expansive mappings and a partial answer to Nirenberg's problem
title_full Notes on expansive mappings and a partial answer to Nirenberg's problem
title_fullStr Notes on expansive mappings and a partial answer to Nirenberg's problem
title_full_unstemmed Notes on expansive mappings and a partial answer to Nirenberg's problem
title_sort notes on expansive mappings and a partial answer to nirenberg's problem
publisher Texas State University
series Electronic Journal of Differential Equations
issn 1072-6691
publishDate 2013-01-01
description 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.
topic Expansive mapping
fixed point
Monotone operator
Nirenberg's problem
url http://ejde.math.txstate.edu/Volumes/2013/02/abstr.html
work_keys_str_mv AT tianxiang notesonexpansivemappingsandapartialanswertonirenbergsproblem
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