“Fixed Point Theorem”的概念、定义、习题解题方法及翻译-数学辞典

单词

Fixed Point Theorem

释义

Fixed Point Theorem

If is a continuous function For All , then has a Fixed Point in .This can be proven by noting that

Since

is continuous, the Intermediate Value Theorem guarantees that there exists a

such that

so there must exist a

such that

so there must exist a Fixed Point

See also Banach Fixed Point Theorem, Brouwer Fixed Point Theorem, Kakutani's Fixed Point Theorem,Lefshetz Fixed Point Formula, Lefshetz Trace Formula, Poincaré-Birkhoff Fixed PointTheorem, Schauder Fixed Point Theorem

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