On solvability of functional equations and system of functional equations arising in dynamic programming. (English) Zbl 1055.39038

Liu, Z.; Agarwal, R. P.; Kang, S. M.

J. Math. Anal. Appl. 297, No. 1, 111-130 (2004).

Authors’ abstract: The purpose of this paper is to study solvability of two classes of functional equations and a class of system of functional equations arising in dynamic programming of multistage decision processes. By using fixed point theorems, a few existence and uniqueness theorems of solutions and iterative approximation for solving these classes of functional equations are established. Under certain conditions, some existence theorems of coincidence solutions for the class of system of functional equations are shown. Some examples are given to demonstrate the advantage of our results than existing ones in the literature.

Reviewer: Claudi Alsina (Barcelona)

MSC:

39B22	Functional equations for real functions
49L20	Dynamic programming in optimal control and differential games
90C39	Dynamic programming

Keywords:

dynamic programming; fixed point theorems; iterative approximation; coincide solutions; nonexpansive mapping; multistage decision process

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