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Properties of Solutions for a Functional Equation Arising in Dynamic Programming

  • Zeqing Liu
  • Haijiang Dong
  • Shin Min Kang
  • Sunhong Lee
Article
  • 231 Downloads

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.

Keywords

Functional equation Dynamic programming Solution Nonexpansive mapping Banach fixed point theorem 

Notes

Acknowledgements

The authors are grateful to the editor and the referees for their valuable comments and suggestions.

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Copyright information

© Springer Science+Business Media New York 2012

Authors and Affiliations

  • Zeqing Liu
    • 1
  • Haijiang Dong
    • 1
  • Shin Min Kang
    • 2
  • Sunhong Lee
    • 2
  1. 1.Department of MathematicsLiaoning Normal UniversityDalianPeople’s Republic of China
  2. 2.Department of Mathematics and RINSGyeongsang National UniversityJinjuKorea

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