Properties of Solutions for a Functional Equation Arising in Dynamic Programming
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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.
KeywordsFunctional equation Dynamic programming Solution Nonexpansive mapping Banach fixed point theorem
The authors are grateful to the editor and the referees for their valuable comments and suggestions.