Article ID: | iaor20132842 |
Volume: | 157 |
Issue: | 3 |
Start Page Number: | 716 |
End Page Number: | 736 |
Publication Date: | Jun 2013 |
Journal: | Journal of Optimization Theory and Applications |
Authors: | Liu Zeqing, Dong Haijiang, Cho Sun, Kang Shin |
Keywords: | programming: dynamic |
This paper deals with a functional equation and inequality arising in dynamic programming of multistage decision processes. Using several fixed‐point theorems due to Krasnoselskii, Boyd–Wong and Liu, we prove the existence and/or uniqueness and iterative approximations of solutions, bounded solutions and bounded continuous solutions for the functional equation in two Banach spaces and a complete metric space, respectively. Utilizing the monotone iterative method, we establish the existence and iterative approximations of solutions and nonpositive solutions for the functional inequality in a complete metric space. Six examples which dwell upon the importance of our results are also included.