名词
中文翻译：巴拿赫定理
同义词：
['Banach fixed-point theorem', 'Banach fixed-point theorem', 'Banach fixed-point theorem']
例句：
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1. The Banach fixed-point theorem states that a contraction mapping is a contraction mapping.
巴拿赫不动点定理表明，一个收缩映射就是一个收缩映射。
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2. In Banach fixed-point theorem, we prove that the function f(x) = x^2 - 1 is a contraction mapping.
在巴拿赫不动点定理中，我们证明了函数f(x) = x^2 - 1是一个收缩映射。
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3. The Banach fixed-point theorem has been widely used in the study of nonlinear programming and optimization problems.
巴拿赫不动点定理在非线性编程和优化问题的研究中得到广泛应用。