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Properties of Solutions for a Functional Equation Arising in Dynamic Programming

Author

Listed:
  • Zeqing Liu

    (Liaoning Normal University)

  • Haijiang Dong

    (Liaoning Normal University)

  • Shin Min Kang

    (Gyeongsang National University)

  • Sunhong Lee

    (Gyeongsang National University)

Abstract

This paper is concerned with a new functional equation arising in dynamic programming of multistage decision processes. Utilizing the Banach fixed point theorem and iterative algorithms, we prove the existence, uniqueness, and iterative approximations of solutions for the functional equation in Banach spaces and a complete metric space, respectively. Some error estimates between the iterative sequences generated by iterative algorithms and the solutions are discussed. Five examples are constructed to illustrate the results presented in this paper.

Suggested Citation

  • Zeqing Liu & Haijiang Dong & Shin Min Kang & Sunhong Lee, 2013. "Properties of Solutions for a Functional Equation Arising in Dynamic Programming," Journal of Optimization Theory and Applications, Springer, vol. 157(3), pages 696-715, June.
    • Handle: RePEc:spr:joptap:v:157:y:2013:i:3:d:10.1007_s10957-012-0191-6
    DOI: 10.1007/s10957-012-0191-6
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    References listed on IDEAS

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    1. Z. Liu & J.S. Ume, 2003. "On Properties of Solutions for a Class of Functional Equations Arising in Dynamic Programming," Journal of Optimization Theory and Applications, Springer, vol. 117(3), pages 533-551, June.
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    2. Deepmala, 2014. "Existence Theorems for Solvability of a Functional Equation Arising in Dynamic Programming," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2014, pages 1-9, April.

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