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Existence Theorems for Solvability of a Functional Equation Arising in Dynamic Programming

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  • Deepmala

Abstract

The paper deals with the existence, uniqueness, and iterative approximations of solutions for the functional equations arising in dynamic programming of multistage decision making processes in Banach spaces BC(S) and B(S) and complete metric space BB(S) , respectively. Our main results extend, improve, and generalize the results due to several authors. Some examples are also given to demonstrate the advantage of our results over existing one in the literature.

Suggested Citation

  • 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.
    • Handle: RePEc:hin:jijmms:706585
    DOI: 10.1155/2014/706585
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    References listed on IDEAS

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    1. Ravi P. Agarwal & Nawab Hussain & Mohamed-Aziz Taoudi, 2012. "Fixed Point Theorems in Ordered Banach Spaces and Applications to Nonlinear Integral Equations," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-15, July.
    2. Richard Bellman, 1957. "On a Dynamic Programming Approach to the Caterer Problem--I," Management Science, INFORMS, vol. 3(3), pages 270-278, April.
    3. 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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