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Properties of Solutions for a Functional Equation Arising in Dynamic Programming

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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.

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Acknowledgements

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

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Authors and Affiliations

  1. Department of Mathematics, Liaoning Normal University, Dalian, Liaoning, 116029, People’s Republic of China

    Zeqing Liu & Haijiang Dong

  2. Department of Mathematics and RINS, Gyeongsang National University, Jinju, 660-701, Korea

    Shin Min Kang & Sunhong Lee

Authors
  1. Zeqing Liu
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  2. Haijiang Dong
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  3. Shin Min Kang
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  4. Sunhong Lee
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Corresponding author

Correspondence to Zeqing Liu.

Additional information

Communicated by Jen-Chih Yao.

This work was supported by the Science Research Foundation of Educational Department of Liaoning Province (L2012380).

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Liu, Z., Dong, H., Kang, S.M. et al. Properties of Solutions for a Functional Equation Arising in Dynamic Programming. J Optim Theory Appl 157, 696–715 (2013). https://doi.org/10.1007/s10957-012-0191-6

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  • DOI: https://doi.org/10.1007/s10957-012-0191-6

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