### On properties of solutions for a functional equation

DOI: http://dx.doi.org/10.12775/TMNA.2015.040

#### Abstract

his paper studies properties of solutions for a functional equation arising in dynamic programming of multistage decision processes. Using the Banach fixed point theorem and the Mann iterative methods, we prove the existence and uniqueness of solutions and convergence of sequences generated by the Mann iterative methods for the functional equation in the Banach spaces $BC(S)$ and $B(S)$ and the complete metric space $BB(S)$, and discuss behaviors of solutions for the functional equation in the complete metric space $BB(S)$. Four examples illustrating the results presented in this paper are also provided.

#### Keywords

Functional equation,dynamic programming, continuous bounded solutions, boundedsolutions, solutions, Mann iterative methods, Banach fixed pointtheorem

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