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Existence and Iterative Approximations of Solutions for Certain Functional Equation and Inequality

Author

Listed:
  • Zeqing Liu

    (Liaoning Normal University)

  • Haijiang Dong

    (Liaoning Normal University)

  • Sun Young Cho

    (Gyeongsang National University)

  • Shin Min Kang

    (Gyeongsang National University)

Abstract

This paper deals with a functional equation and inequality arising in dynamic programming of multistage decision processes. Using several fixed-point theorems due to Krasnoselskii, Boyd–Wong and Liu, we prove the existence and/or uniqueness and iterative approximations of solutions, bounded solutions and bounded continuous solutions for the functional equation in two Banach spaces and a complete metric space, respectively. Utilizing the monotone iterative method, we establish the existence and iterative approximations of solutions and nonpositive solutions for the functional inequality in a complete metric space. Six examples which dwell upon the importance of our results are also included.

Suggested Citation

  • Zeqing Liu & Haijiang Dong & Sun Young Cho & Shin Min Kang, 2013. "Existence and Iterative Approximations of Solutions for Certain Functional Equation and Inequality," Journal of Optimization Theory and Applications, Springer, vol. 157(3), pages 716-736, June.
    • Handle: RePEc:spr:joptap:v:157:y:2013:i:3:d:10.1007_s10957-012-0185-4
    DOI: 10.1007/s10957-012-0185-4
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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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