一类动态规划问题的收益函数存在定理

Some existence theorems of benefit function in dynamic programming

给出完备度量空间非扩张算子的一个不动点定理,应用它研究动态规划中出现的一类泛函方程,得到了最优指标函数的存在惟一性定理和函数空间近似解的误差估计,推广和改进了已有的某些结果.

The theory of fixed point is applied to the equations arising in the dynamic programming and the existence and uniqueness theorems on benefit function are obtained. Monotone decreasing operations in complete lattice is discussed in the paper and error on which unction sequence approximate the solution is evaluated.