ID 41533
JaLCDOI
Sort Key
5
FullText URL
Author
Fujimoto, Takao
Ranade, Ravindra R.
Abstract
This note is aimed at presenting an easy and simple proposition on the univalence of a given nonlinear differentiable mapping whose Jacobian matrix has sign-regularity. First the notion of sign-regularity of Jacobian matrix on a domain is defined. We classifY the sign patterns into four categories: plus, minus, zero, and the rest. The plus sign is given to the (i, j) entry of the Jacobian matrix when the i-th component function is always increasing with respect to the j-th coordinate variable, the negative sign when the function is always decreasing, and the sign of zero when the function does not include the j-th coordinate variable. Otherwise, the sign is set as an asterisk *. Our proof is simple and elementary by use ofthe mean value theorem. In the final section, we give a list of our future research topics, some of which are under way. Especially a generalization to discontinuous mappings should be interesting.
Note
研究ノート (Note)
Publication Title
岡山大学経済学会雑誌
Published Date
1998-06-10
Volume
volume30
Issue
issue1
Publisher
岡山大学経済学会
Publisher Alternative
The Economic Association of Okayama University
Start Page
111
End Page
116
ISSN
0386-3069
NCID
AN00032897
Content Type
Journal Article
OAI-PMH Set
岡山大学
language
英語
File Version
publisher
NAID
Eprints Journal Name
oer