On properties of solutions for a functional equation

Abstract

This paper studies properties of solutions for afunctional equation arising in dynamic programming of multistagedecision processes. Using the Banach fixed point theorem and theMann iterative methods, we prove the existence and uniqueness ofsolutions and convergence of sequences generated by the Manniterative methods for the functional equation in the Banach spaces$BC(S)$ and $B(S)$ and the complete metric space $BB(S)$, anddiscuss behaviors of solutions for the functional equation in thecomplete metric space $BB(S)$. Four examples illustrating theresults presented in this paper are also provided.