1. Different research objects: fixed point theory mainly focuses on fixed points of functions or mappings, while other mathematical theories may focus on a wider range of objects, such as sequences, matrices, geometric figures, etc.
2. Different research methods: Iterative method, approximation method and algebraic method are usually used in the study of fixed point theory, while other mathematical theories may adopt different methods such as calculus, linear algebra and probability theory.
3. Different application fields: The fixed point theory is widely used in many fields, such as differential equations, dynamical systems, optimization problems, economics and so on. And other mathematical theories may be more widely used in some specific fields.
4. Different theoretical bases: The theoretical bases of fixed point theory mainly include topology, functional analysis, algebra and so on. Other mathematical theories may be based on different branches of mathematics, such as geometry, combinatorial mathematics, probability theory, etc.
5. The nature of the problem is different: the problems studied by the fixed point theory are usually abstract and universal, while other mathematical theories may pay more attention to the solution and application of specific problems.
In a word, the fixed point theory is different from other mathematical theories in research object, research method, application field, theoretical basis, nature of problems and so on. However, these different mathematical theories are often interrelated and cross-cutting, and the identity of * * * constitutes a huge and rich mathematical discipline system.