Research On Iterative Problem Of Several Types Functions In Topological Space

A great breakthrough has been made in the mapping iteration problem after the improvement of the physical engineering science, differential and difference equations and computer condition. We can predict the development of things through the research of iterative. That is why we need to highlight the mapping iteration. However, one of the most basic function iteration theory problems is iterated function and iterative cycle.This paper mainly studies several kinds of one-dimensional function of iteration formula by using fixed point method, recursive method, mathematical induction method, conjugate similarity method, sequence method, and mainly using fixed point method, recursive method, mathematical induction method, similar to the conjugate method, method of sequence for several classes of one-dimensional function iteration formula, as well as the study of the two dimensional iterative mapping by using difference equation. The author discusses the iterative estimation of function of f(x)= cosx by introducing the function property of self mapping iteration, leading out the iterative inequality of f(x)= cosx.And then, the iterative estimation is applied to solve a class of problems related to the number of sequences. Finally, the convergence and periodicity of the linear fractional function iteration are studied. This paper consists of five chapters. The first chapter mainly introduces the background and the research status of functional iterative estimation. The second chapter obtains the iterative formula of several different functions by applying different methods of function iteration, and studies the first question raised by Schroder:how do we write a more obvious expression of the fn(x). The third chapter discusses the iterative estimation of a class of functions, and solves a series of related problems based on the functional properties of self mapping iteration. The fourth chapter discusses the convergence problem of the iterative linear fractional function, and describes the iterative periodicity of the linear fractional function, and studies the strongest and most significant character of the functional recovery by finding the relation between the characteristic value and the fixed point of the linear fractional function. The fifth chapter summarizes the content of this paper, and has a vision the future research and development of functional iterative estimation.