连续函数压缩映射问题的讨论

On the Contraction Mapping Principle of Continuous Functions

就连续函数应用问题的教学内容进行探讨.介绍数列和连续函数的压缩映射原理及其在方程求解,数学建模等方面的应用,并给出压缩映射的一般形式,续而通过压缩映射原理在图像处理和导航系统中的应用,阐明创新思想的重要性,以求开拓学生的思路和想象空间.

This paper discusses teaching contents of applications of continuous functions. The contraction mapping principles for sequences and functions are introduced, and their applications in equation solving and mathematical modeling are discussed. A more general form of the principle and its application in image processing and navigation system are shown. We wish to provide broader views and ideas for our students.