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The Schur and Samuelson Conditions for a Cubic Equation

Author

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  • Okuguchi, Koji
  • Irie, Kazuya

Abstract

The Schur conditions for the moduli of the roots for a cubic equation to be less than one are expressed as a set of inequalities that does not involve determinants, and a direct demonstration of the equivalence of the Schur and Samuelson-Farebrother conditions is given on the basis of a diagrammatic argument. Copyright 1990 by Blackwell Publishers Ltd and The Victoria University of Manchester

Suggested Citation

  • Okuguchi, Koji & Irie, Kazuya, 1990. "The Schur and Samuelson Conditions for a Cubic Equation," The Manchester School of Economic & Social Studies, University of Manchester, vol. 58(4), pages 414-418, December.
    • Handle: RePEc:bla:manch2:v:58:y:1990:i:4:p:414-18
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    Cited by:

    1. Fabio Tramontana & Laura Gardini & Roberto Dieci & Frank Westerhoff, 2009. "The Emergence of Bull and Bear Dynamics in a Nonlinear Model of Interacting Markets," Discrete Dynamics in Nature and Society, Hindawi, vol. 2009, pages 1-30, July.
    2. Laura Gardini & Noemi Schmitt & Iryna Sushko & Fabio Tramontana & Frank Westerhoff, 2019. "Necessary and sufficient conditions for the roots of a cubic polynomial and bifurcations of codimension-1, -2, -3 for 3D maps," Working Papers 1908, University of Urbino Carlo Bo, Department of Economics, Society & Politics - Scientific Committee - L. Stefanini & G. Travaglini, revised 2019.
    3. Akio Matsumoto & Ferenc Szidarovszky, 2014. "Discrete-time delay dynamics of boundedly rational monopoly," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 37(1), pages 53-79, April.
    4. Matsumoto, Akio & Szidarovszky, Ferenc, 2014. "Complex dynamics of monopolies with gradient adjustment," Economic Modelling, Elsevier, vol. 42(C), pages 220-229.
    5. Amer Tabakovic, 2015. "On the Characterization of Steady-States in Three-Dimensional Discrete Dynamical Systems," DEM Discussion Paper Series 15-16, Department of Economics at the University of Luxembourg.
    6. Elsadany, A.A., 2012. "Competition analysis of a triopoly game with bounded rationality," Chaos, Solitons & Fractals, Elsevier, vol. 45(11), pages 1343-1348.
    7. Takeshi Yamazaki, 2016. "On the Works of Professor Koji Okuguchi," Springer Series in Game Theory, in: Pierre von Mouche & Federico Quartieri (ed.), Equilibrium Theory for Cournot Oligopolies and Related Games, pages 7-13, Springer.

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