The Study On The Properties Of Solutions To The Combinational Functional Equations Arising From Dynamic Programming

In recent years, the discussion of the existence, uniqueness and iterative approximationof solutions to a class of functional equations arising from dynamic programming ofmultistage decision processes has become more and more popular. Based on the study of theexistence, uniqueness and iterative approximation of solutions to basic form functionalequations, it is not difficult to find that we don’t have to place restrictions on the basic formequations. Therefore, by combining the results of functional equations with basic form studiedbefore and by using the fixed point theorem, and a new kind of combinational thinking, werewrite the basic forms of functional equations, and three kinds of more complex functionalequations are introduced in this paper, and the existence, uniqueness, iterative approximationand other relevant important properties of the solutions to the corresponding equations arediscussed. This paper is organized as follows:The first chapter is the introduction, in which the research background of this article andthe problems of our research are introduced.In the second chapter, we study the existence of the solutions to the combinationalfunctional equation which takes the supremum together and contains the parameterAnd the sufficient conditions for the existence and uniqueness of solution are obtained, inaddition, some properties of the solutions are given.In the third chapter, based on the discussion before, we study the existence and theproperties of the solutions to the combinational functional equation which takes the infimumtogether and contains the parameterAnd a new property of the solutions is given.In the last chapter, according to the previous analysis for the properties of solutions tothe combinational functional equation, we discuss the existence and the properties of thecombinational functional equation which combine two kinds of dual functions which takesupremum and infimum separately Based on the research of the properties of the solutions to several kinds of functionalequations, the results we obtained not only expand the range of research, but also can beutilized to solve more practical problems in broader areas.