Hostname: page-component-848d4c4894-x5gtn Total loading time: 0 Render date: 2024-06-02T12:46:51.413Z Has data issue: false hasContentIssue false
  • English
  • Français

On time dependent multistep dynamic processes

Published online by Cambridge University Press:  17 April 2009

Ferenc Szidarovszky  and
Ioannis K. Argyros
Ferenc Szidarovszky
Affiliation:
Department of Systems and Industrial Engineering, University of Arizona, Tucson, AZ 85721, United States of America
Ioannis K. Argyros
Affiliation:
Department of Mathematics, Cameron University, Lawton OK 73505-6377, United States of America
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

The discrete time scale Liapunov theory is extended to time dependent, higher order, nonlinear difference equations in a partially ordered topological space. The monotone convergence of the solution is examined and the speed of convergence is estimated.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 43 , Issue 1 , February 1991 , pp. 51 - 61
Copyright
Copyright © Australian Mathematical Society 1991

References

[1]Brock, W.A. and Scheinkman, J.A., ‘Some results on global asymptotic stability of difference equations’, J. Econom. Theory 10 (1975), 265–268.Google Scholar
[2]Chander, P., ‘The nonlinear input-output model’, J. Econom. Theory 30 (1983), 219–229.CrossRefGoogle Scholar
[3]Chien, M.J. and Chan, L., ‘Nonlinear input-output model with piecewise affice coefficients’, J. Econom. Theory 21 (1979), 389–410.Google Scholar
[4]Fujimoto, T., ‘Asymptotic stability of non-linear difference equations’, Econom. Lett. 22 (1987), 247–250.CrossRefGoogle Scholar
[5]Fujimoto, T., ‘Global asymptotic stability of non-linear difference equations II’, Econom. Lett. 23 (1987), 275–277.Google Scholar
[6]Okuguchi, K. and Szidarovszky, F., ‘On a nonlinear input-output system’, Math. Social Sci. 13 (1987), 277–281.Google Scholar
[7]Okuguchi, K. and Szidarovszky, F. (to appear), The Theory of Oliogopoly with Multi-Product Firms (Springer-Verlag, New York, Heidelberg, Berlin, 1990 to appear).CrossRefGoogle Scholar
[8]Ortega, J.M. and Rheinboldt, W.C., Iterative Solutions of Non-Linear Equations in Several Varibles (Academic Press, New York, London, 1970).Google Scholar
[9]Redheffer, R. and Walter, W., ‘A comparison theorem for difference inequalities’, J. of Differential Equations 44 (1982), 111–117.Google Scholar
[10]Szidarovszky, F. and Okuguchi, K., ‘A note on global asymptotic stability of non-linear difference equations’, Econom. Lett. 26 (1988), 349–352.Google Scholar
[11]Szidarovszky, F. and Yakowitz, S., Principles and Procedures of Numerical Analysis (Plenum Press, New York, London, 1978).CrossRefGoogle Scholar
[12]Uzawa, H., ‘The Stability of Dynamic Processes’, Econometrica 29 (1961), 617–631.Google Scholar
[13]Vandergraft, J.S., ‘Newton's method for convex operators in partially ordered spaces’, SIAM J. Numer. Anal. 4 (1967), 406–432.CrossRefGoogle Scholar
[14]Wilson, H.K., Ordinary Differential Equations (Addison Wesley, Reading, Mass., 1971).Google Scholar
[15]Zangwill, W.I., Nonlinear Programming. A Unified Approach (Prentice-Hall, Englewood Cliffs, N.J., 1969).Google Scholar