Schauder's fixed-point theorem
Schauder's fixed-point theorem
[¦shau̇d·ərz ¦fikst ‚pȯint ′thir·əm] (mathematics)
A continuous mapping from a closed, compact, convex set in a Banach space into itself has at least one fixed point.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.
References in periodicals archive
On the other hand, the operator [[PSI].sub.k] : [U.sub.k] [right arrow] [U.sub.k] is completely continuous by Lemma 10; then by
Schauder's fixed-point Theorem 11, each problem of (1)-(3) has a solution.
We next introduce Schauder's fixed-point theorem used to prove the existence of a solution to (4) and (5).
We next show the existence of a solution to (4) by the following Schauder's fixed-point theorem.
By Schauder's fixed-point theorem, we can conclude that problem (4) has at least one solution.
Copyright © 2003-2025 Farlex, Inc
Disclaimer
All content on this website, including dictionary, thesaurus, literature, geography, and other reference data is for informational purposes only. This information should not be considered complete, up to date, and is not intended to be used in place of a visit, consultation, or advice of a legal, medical, or any other professional.