This paper introduces the concept and significance of fixed point in mathematics through a small experiment. This paper mainly introduces the most important Banach fixed point theory, that is, the contraction mapping principle, and then understands some properties of the fixed point principle by learning, and uses the contraction fixed point principle to solve the existence and uniqueness of solutions in differential equations, integral equations and algebraic equations. At the same time, a series of problems such as the limit of sequence are solved by using the transformation form of compressed fixed point principle.

This paper deduces the concept and significance of fixed point through a small experiment in mathematics. This paper mainly introduces the most important theory of fixed point theory, the principle of fixed point Banach contraction mapping, and then through the study of fixed point theorem, we can understand the fixed point theorem, and use some properties of fixed point theorem to solve the existence and uniqueness of solutions of differential equations, integral equations and algebraic equations. At the same time, the fixed point theorem of transformation form is used to solve the problems of sequence limit.