Bibliographic Information
- Other Title
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- A Note on Qualitative Economics for Uni
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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.
Journal
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- 岡山大学経済学会雑誌
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岡山大学経済学会雑誌 30 (1), 111-116, 1998-06-10
岡山大学経済学会
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Details 詳細情報について
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- CRID
- 1390572174502244736
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- NII Article ID
- 110000129990
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- NII Book ID
- AN00032897
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- ISSN
- 03863069
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- NDL BIB ID
- 4476284
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- Text Lang
- en
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- Data Source
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- JaLC
- IRDB
- NDL
- CiNii Articles