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The Schauder fixed point theorem is an extension of the Brouwer fixed point theorem to topological vector spaces, which may be of infinite dimension. It asserts that if is a nonempty convex subset of a Hausdorff topological vector space and is a continuous mapping of into itself such that is contained in a compact subset of , then has a fixed point. Let be a continuous and compact mapping of a Banach space into itself, such that the set is bounded. Then has a fixed point.

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• Schauder fixed point theorem
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• The Schauder fixed point theorem is an extension of the Brouwer fixed point theorem to topological vector spaces, which may be of infinite dimension. It asserts that if is a nonempty convex subset of a Hausdorff topological vector space and is a continuous mapping of into itself such that is contained in a compact subset of , then has a fixed point. Let be a continuous and compact mapping of a Banach space into itself, such that the set is bounded. Then has a fixed point.
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• The Schauder fixed point theorem is an extension of the Brouwer fixed point theorem to topological vector spaces, which may be of infinite dimension. It asserts that if is a nonempty convex subset of a Hausdorff topological vector space and is a continuous mapping of into itself such that is contained in a compact subset of , then has a fixed point. A consequence, called Schaefer's fixed point theorem, is particularly useful for proving existence of solutions to nonlinear partial differential equations.Schaefer's theorem is in fact a special case of the far reaching Leray–Schauder theorem which was discovered earlier by Juliusz Schauder and Jean Leray.The statement is as follows: Let be a continuous and compact mapping of a Banach space into itself, such that the set is bounded. Then has a fixed point.
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• Schauder fixed point theorem
• Schauder theorem
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