On Krasnoselskii's Cone Fixed Point Theorem
By Man Kam Kwong. 2008
53 citations recorded by the source corpus.
In recent years, the Krasnoselskii fixed point theorem for cone maps and its many generalizations have been successfully applied to establish the existence of multiple solutions in the study of boundary value problems of various types. In the first part of this paper, we revisit the Krasnoselskii theorem, in a more topological perspective, and show that it can be deduced in an elementary way from the classical Brouwer-Schauder theorem. This viewpoint also leads to a topology-theoretic generalization of the theorem. In the second part of the paper, we extend the cone theorem in a different direction using the notion of retraction and show that a stronger form of the often cited Leggett-Williams theorem is a special case of this extension.
Subfields: Astronomy and Astrophysics, Computational Theory and Mathematics, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/b79d8b16b9e4a7aa0f5fedff4239138606bf6cd5
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Astronomy and Astrophysics
In Computational Theory and Mathematics
In Geometry and Topology
Citations in the corpus
- Positive solutions of q-difference equation (2009, methodology): “The authors used a Fixed Point Theorem of Krasnoselskii; see [7].”