Solvability and convergence of iterative algorithms for certain functional equations arising in dynamic programming

Abstract

In this article, we introduce and study the following functional equation arising in dynamic programming of multistage decision processes: In order to solve the functional equation, we suggest some iterative algorithms. Under certain conditions we give a few sufficient conditions ensuring both the existence and uniqueness of solution for the functional equation and the convergence of these iterative algorithms with respect to the solution. We investigate also properties of nonpositive solutions and nonnegative solutions for several functional equations which are special cases of the above mentioned functional equation. To illustrate the results presented in this article, we construct eight nontrivial examples.