Existence and uniqueness of solutions of functional equations arising in dynamic programming

In this paper, we study solvability of two functional equations arising in dynamic programming of multistage decision processes. By using Boyd and Wong fixed point theorem, some existence and uniqueness theorems of solutions and iterative approximation for solving these class of functional equations are established. The results presented here extend, improve and unify the corresponding results due to Bellman, Bhakta and Mitra, Bhakta and Choudhary, Liu and Kang, Liu et al., Jiang et al. and others. We also discuss some illustrative examples to highlight the realized improvements.