Some existence theorems for functional equations and system of functional equations arising in dynamic programming. (English) Zbl 1215.49008

Liu, Zeqing; Ume, Jeong Sheok; Kang, Shin Min

Taiwanese J. Math. 14, No. 4, 1517-1536 (2010).

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

Keywords:

dynamic programming; functional equation; system of functional equations

Citations:

Zbl 0533.90091; Zbl 1018.90064