Sur les opérations dans les ensembles abstraits et leur application aux équations intégrales.

Banach, S. (1922). Sur les opérations dans les ensembles abstraits et leur application aux équations intégrales. Fundamenta Mathematicae, 3, 133-181.

Type

Journal article

Intellectual base

Primary research

Year

1922

Volume

3

Pages

133-181

DOI

10.4064/fm-3-1-133-181

DOI registrant

Institute of Mathematics, Polish Academy of Sciences

Link

https://eudml.org/doc/213289

Cited from

mathematics

Cited by

3 citations across 3 artifacts.

Each citation links to the sentence it supports in the citing article.

Primes

• Completeness
  • The five canonical varieties —

    This sourceDefinition of Banach spaces as complete normed vector spaces, establishing completeness as a foundational property for functional analysis.

• Fixed Point
  • Existence can be certified by structural conditions: a contractive map on a complete space has a unique attracting fixed point, and a continuous self-map of a convex compact set has at least one, so the existence of a resting state can be guaranteed before it is located.
• Metric
  • The fixed-point theorem for contractions — every contraction on a complete metric space has a unique fixed point — fires identically in numerical iteration, in dynamic-programming value iteration, in iterated-function-system image compression, and in proofs of economic-equilibrium existence.

Verification

Does it exist? Confirmed. This work's DOI resolves to a registered record, which fixes its identity. That is all it fixes.

Does it back the claim? Not recorded. Neither this nor any other of the 3 citations of this work carries a recorded support check.

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Links previously used in the corpus

Before the registry existed this work was also linked 1 other way.

• https://doi.org/10.4064/fm-3-1-133-181 ×2

Registry ID ref:c2c885cbbc42 · see in the full table