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ID 41533
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)
Published Date
1998-06-10
Publication Title
岡山大学経済学会雑誌
Publication Title Alternative
Okayama Economic Review
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
language
英語
File Version
publisher
Refereed
True
Eprints Journal Name
oer