源于动态规划的组合型泛函方程解的研究

近年来,对于源于多目标决策过程动态规划的泛函方程在某种特定条件下解的存在性,唯一性以及迭代逼近的研究越来越广泛.然而,通过对这类问题的研究,不难发现泛函方程的类型不必局限于它的基本形式.因此,结合之前对于基本形式下泛函方程的研究成果,本文利用不动点定理以及一种新的组合性思维,研究了一类更加复杂的泛函方程,即f（x）=λsup∈D{u（x,y）＋f（T（x,y））}＋（1-λ）infy∈D{v（x,y）＋f）T,（x,y））},x∈S,其中λ∈[0,1]的解的性质,这类泛函方程的引入扩大了研究问题的范围,同时可以用它来解决更多的实际问题.

The Research of Solutions for Combination Functional Equations Arising in Dynamic Programming

In recent years, the discussion of the existence, uniqueness and iterative approximation of solutions to a class of functional equations arising in dynamic programming of multistage decision processes has become more and more popular. With the study of these functional equations, we found that the research doesn＇t have to be restricted by on the basic form, therefore, by combining the results of functional equations with basic form studied before and by using the fixed point theorem, a new kind of more complex functional equation is introduced in this paper, namely f（x）=λsup∈D{u（x,y）＋f（T（x,y））}＋（1-λ）infy∈D{v（x,y）＋f）T,（x,y））},x∈S,其中λ∈[0,1] The results obtained in this paper expand the range of researeh and can be utilized to solve more practical problems.