References
Alexandroff, P., andH. Hopf: Topologie I. 636 pp. Berlin: Julius Springer 1935.
Hawkins, D., andH. A. Simon: Some conditions of macroeconomic stability. Econometrica17, 1949.
McKenzie, L. W.: Matrices with dominant diagonals and economic theory. Mathematical Methods in the Social Sciences 1959. Stanford Univ. Press 1960.
Noshiro, K.: On the theory of schlicht functions. J. Faculty Sci. Hokkaido Imp. Univ.2 (1934).
Samuelson, P. A.: Prices of factors and goods in general equilibrium. Rev. Econ. Stud.21 (1953).
Stiemke, E.: Über positive Lösungen homogener linearer Gleichungen. Math. Ann.76, (1915).
Tucker, A. W.: Dual systems of homogeneous linear relations. “Linear Inequalities and Related Systems.” Ann. Math. Studies No. 38. Princeton Univ. Press 1956.
Author information
Authors and Affiliations
Additional information
This paper is based on a joint research done by the both authors at the Institute of Social and Economic Research, Osaka University. The first author is supported in part by a contract with the Office of Naval Research, USA. The authors benefited from valuable correspondence with ProfessorP. A. Samuelson.
Rights and permissions
About this article
Cite this article
Gale, D., Nikaido, H. The Jacobian matrix and global univalence of mappings. Math. Ann. 159, 81–93 (1965). https://doi.org/10.1007/BF01360282
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/BF01360282