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Some existence theorems for functional equations and system of functional equations arising in dynamic programming. (English) Zbl 1215.49008
Summary: We study the existence, uniqueness and iterative approximation of solutions for a few classes of functional equations arising in dynamic programming of multistage decision processes. By using monotone iterative methods, we also establish the existence and iterative approximation of coincidence solutions for certain kinds of system of functional equations. The results presented in this paper extend, improve and unify the results due to P. C. Bhakta and S. Mitra [J. Math. Anal. Appl. 98, 348–362 (1984; Zbl 0533.90091)], S. S. Chang [“Some existence theorems of common and coincidence solutions for a class of functional equations arising in dynamic programming”, Appl. Math. Mechanics 12, 31–37 (1991)] and Z. Liu [J. Math. Anal. Appl. 262, No. 2, 529–553 (2001; Zbl 1018.90064)] and others.

MSC:
49J21 Existence theories for optimal control problems involving relations other than differential equations
49L20 Dynamic programming in optimal control and differential games
49L99 Hamilton-Jacobi theories
90C39 Dynamic programming
47J25 Iterative procedures involving nonlinear operators
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