A class of globally univalent differentiable mappings

Czesław Olech; Thiruvenkatachari Parthasarathy; G. Ravindran

Archivum Mathematicum (1990)

  • Volume: 026, Issue: 2-3, page 165-172
  • ISSN: 0044-8753

How to cite


Olech, Czesław, Parthasarathy, Thiruvenkatachari, and Ravindran, G.. "A class of globally univalent differentiable mappings." Archivum Mathematicum 026.2-3 (1990): 165-172. <http://eudml.org/doc/18298>.

author = {Olech, Czesław, Parthasarathy, Thiruvenkatachari, Ravindran, G.},
journal = {Archivum Mathematicum},
keywords = {univalence; almost P-matrix; almost N-matrix; differentiable mapping; Jacobian matrix},
language = {eng},
number = {2-3},
pages = {165-172},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {A class of globally univalent differentiable mappings},
url = {http://eudml.org/doc/18298},
volume = {026},
year = {1990},

AU - Olech, Czesław
AU - Parthasarathy, Thiruvenkatachari
AU - Ravindran, G.
TI - A class of globally univalent differentiable mappings
JO - Archivum Mathematicum
PY - 1990
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 026
IS - 2-3
SP - 165
EP - 172
LA - eng
KW - univalence; almost P-matrix; almost N-matrix; differentiable mapping; Jacobian matrix
UR - http://eudml.org/doc/18298
ER -


  1. D. Gale, The theory of linear economic models, McGгawHill - New York, 1960. (1960) Zbl0114.12203MR0115801
  2. D. Gale, H. Nikaido, The Jacobian matrix and global univalence of mapping, Math. Ann., 159 (1965), 81-93. (1965) Zbl0158.04903MR0204592
  3. C. B. Garcia, W. I. Zangwill, On univalence and P-matrices, Lin. Alg. and its Appl., 24 (1979), 239-250. (1979) Zbl0404.90090MR0524840
  4. A. Granas, J. Dugundji, Fixed point theory, Vol. I, PWN Warszawa 1982. (1982) Zbl0483.47038MR0660439
  5. K. Inada, The product coefficient matrix and the Stolper-Samuelson condition, Econometrica 39 (1971), 219-235. (1971) Zbl0224.90010MR0452537
  6. K. Kuratowski, Topology vol. I, Academic Press - New York -San Francisco-London, 1969. (1969) MR0217751
  7. A. Mas-Colell, Homeomorphisms of compact convex sets and the Jacobian matrix, SIAM J. Math. Anal. 10 (1966), 1105-1109. (1966) MR0547799
  8. G. H. Meisteгs, C. Olech, A Jacobian condition for injectivity of differentiable plane maps, to appeaг in Ann. Math. Polon. 
  9. C. Olech, On the global stability of an autonomous system on the plane, Contribution to Diff. Eq. 1 (1963), 389-400. (1963) Zbl0136.08602MR0147734
  10. T. Parthasarathy, On global univalence theorems, Lecture Notes in Mathematics 977, Springer-Verlag, Berlin-Heidelberg-New York 1983. (1983) Zbl0506.90001MR0694845
  11. T. Parthasarathy, G. Ravindran, The Jacobian matrix, global univalence and completely mixed games, Math. O. R. 11 (1986), 663-671. (1986) Zbl0652.26016MR0865561
  12. T. Parthasarathy, G. Ravindran, N-matrices, Preprint, Indian Statistical Institute, New Delhi 1989. (1989) Zbl0732.15008MR1071701
  13. G. Ravindran, Completely mixed games, Jacobian matrix and univalence, J. of Orissa Math. Soc., 4 (1985), 129-140. (1985) Zbl0644.26012MR0950467
  14. T. Ważewski, Sur l'évaluation du domaine d'existence des fonctions implicites réelles ou complexes, Annal. de la Société Polonaise de Mathématique, 20 (1947), 81-120. (1947) Zbl0032.05601MR0026100

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