... 1999 11 Z Liu and J S Ume, On properties of solutions for a class of functional equations arising in dynamic programming,” Journal of Optimization Theory and Applications, vol 117, no 3, pp 533–551, ... The aim of this paper is to investigate properties of solutions for the following more general functional equations arising in dynamic programming of multistage decision processes: f x opt p x, ... theorems for functional equations arising in dynamic programming,” Journal of Mathematical Analysis and Applications, vol 98, no 2, pp 348–362, 1984 Z Liu, “Existence theorems of solutions for certain...