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Statistical Convergence and Turnpike Theory

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Encyclopedia of Optimization
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Article Outline

Keywords and Phrases

Introduction

Turnpike Theory

Statistical Cluster Points and Statistical Convergence

Problem 1

Problem 2

A Challenging Problem

See also

References

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References

  1. Buck RC (1953) Generalized asymptotic density. Am J Math 75:335–346

    Article  MathSciNet  MATH  Google Scholar 

  2. Connor JS (1988) The statistical and strong p-Cesaro convergence of sequences. Analysis 8:47–63

    MathSciNet  MATH  Google Scholar 

  3. Dorfman R, Samuelson PA, Solow RM (1958) Linear Programming and Economic Analysis. McGraw Hill, New York

    MATH  Google Scholar 

  4. Fast H (1951) Sur la convergence statistique. Colloq Math 2:241–244

    MathSciNet  MATH  Google Scholar 

  5. Fridy JA (1985) On statistical convergence. Analysis 5:301–313

    MathSciNet  MATH  Google Scholar 

  6. Fridy JA (1993) Statistical limit points. Proc Am Math Soc 4:1187–1192

    Article  MathSciNet  Google Scholar 

  7. Maddox IJ (1988) Statistical convergence in a locally convex sequence space. Math Proc Camp Phil Soc 104:141–145

    Article  MathSciNet  MATH  Google Scholar 

  8. Makarov VL, Rubinov AM (1977) Mathematical Theory of Economic Dynamics and Equilibria. Springer, New York

    MATH  Google Scholar 

  9. Mamedov MA (1985) Asymptotical optimal paths in models with environment pollution being taken into account. Optimization, Novosibirsk 36(53):101–112

    Google Scholar 

  10. Mamedov MA (1992) Turnpike theorems in continuous systems with integral functionals. Russ Acad Sci Dokl Math 45(2):432–435

    Google Scholar 

  11. Mamedov MA (1993) Turnpike theorems for integral functionals. Russ Acad Sci Dokl Math 46(1):174–177

    Google Scholar 

  12. Mamedov MA (2003) Turnpike Theorem for Continuous-time Control Systems when Optimal Stationary Point is not unique. Abstr Appl Anal 11:631–650

    Article  Google Scholar 

  13. Mamedov MA, Borisov KY (1988) A simple model of economic grow and pollution control. Vestn Leningr Univ, 5(5):120–124

    Google Scholar 

  14. Mamedov MA, Pehlivan S (2000) Statistical convergence of optimal paths. Math Jpn 52(1):51–55

    Article  MathSciNet  MATH  Google Scholar 

  15. Mamedov MA, Pehlivan S (2001) Statistical cluster points and turnpike theorem in nonconvex problems. J Math Anal Appl 256:686–693

    Article  MathSciNet  MATH  Google Scholar 

  16. McKenzie LW (1976) Turnpike theory. Econometrica 44:841–866

    Article  MathSciNet  MATH  Google Scholar 

  17. von Neumann J (1945–1946) A Model of General Economic Equilibrium. Rev Econ Stud 13:1–9

    Google Scholar 

  18. Panasyuk AI, Panasyuk VI (1986) Asymptotic turnpike optimization of control systems. Nauka Techn

    Google Scholar 

  19. Pehlivan S, Mamedov MA (2000) Statistical cluster points and turnpike. Optimization 48:93–106

    Article  MathSciNet  MATH  Google Scholar 

  20. Rockafellar RT (1973) Saddle points of Hamiltonian systems in convex problems of Lagrange. J Optim Theory Appl 12:367–390

    Article  MathSciNet  MATH  Google Scholar 

  21. Rockafellar RT (1976) Saddle points of Hamiltonian systems in convex problems having a nonzero discount rate. J Econ Theory 12:71–113

    Article  MathSciNet  MATH  Google Scholar 

  22. Śalăt T (1980) On statistically convergent sequences of real numbers. Math Slovaca 30:139–150

    MathSciNet  MATH  Google Scholar 

  23. Steinhaus H (1951) Sur la convergence ordinarie et la convergence asymptotique. Colloq Math 2:73–74

    MathSciNet  Google Scholar 

  24. Scheinkman JA (1976) On optimal steady states of n-sector growth models when utility is discounted. J Econ Theory 12:11–30

    Article  MathSciNet  MATH  Google Scholar 

  25. Zaslavski A (2005) Turnpike Properties in the Calculus of Variations and Optimal Control. Series: Nonconvex Optimization and Its Applications, vol 80 XXII. Springer, New York, p 396

    Google Scholar 

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Mammadov (Mamedov), M. (2008). Statistical Convergence and Turnpike Theory . In: Floudas, C., Pardalos, P. (eds) Encyclopedia of Optimization. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-74759-0_643

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