On Properties of Solutions for Two Functional Equations Arising in Dynamic Programming

Fixexd point theory and applications

JeongSheok Ume¹  ShinMin Kang²  Zeqing Liu³ 

[1]Department of Applied Mathematics, Changwon National University, Changwon, Republic of Korea

[2]Department of Mathematics and Research Institute of Natural Science, Gyeongsang National University, Chinju, Republic of Korea

[3]Department of Mathematics, Liaoning Normal University, Dalian, China

关键词: Positive Integer;    State Space;    Unique Solution;    Functional Equation;    Dynamic Programming;   

DOI  :  10.1155/2010/905858

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

We introduce and study two new functional equations, which contain a lot of known functional equations as special cases, arising in dynamic programming of multistage decision processes. By applying a new fixed point theorem, we obtain the existence, uniqueness, iterative approximation, and error estimate of solutions for these functional equations. Under certain conditions, we also study properties of solutions for one of the functional equations. The results presented in this paper extend, improve, and unify the results according to Bellman, Bellman and Roosta, Bhakta and Choudhury, Bhakta and Mitra, Liu, Liu and Ume, and others. Two examples are given to demonstrate the advantage of our results over existing results in the literature.

【 授权许可】

CC BY