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On Darbo's fixed point principle.
- Source :
- Moroccan Journal of Pure & Applied Analysis; Sep2023, Vol. 9 Issue 3, p304-310, 7p
- Publication Year :
- 2023
-
Abstract
- In this paper, we prove the following generalization of the classical Darbo fixed point principle : Let X be a Banach space and µ be a montone measure of noncompactness on X which satisfies the generalized Cantor intersection property. Let C be a nonempty bounded closed convex subset of X and T : C → C be a continuous mapping such that for any countable set Ω ⊂ C, we have µ(T(Ω)) ≤ kµ(Ω), where k is a constant, 0 ≤ k < 1. Then T has at least one fixed point in C. The proof is based on a combined use of topological methods and partial ordering techniques and relies on the Schauder and the Knaster-Tarski fixed point principles. [ABSTRACT FROM AUTHOR]
- Subjects :
- FIXED point theory
BANACH spaces
INTERSECTION theory
CONVEX sets
NONLINEAR operators
Subjects
Details
- Language :
- English
- ISSN :
- 23518227
- Volume :
- 9
- Issue :
- 3
- Database :
- Complementary Index
- Journal :
- Moroccan Journal of Pure & Applied Analysis
- Publication Type :
- Academic Journal
- Accession number :
- 175367231
- Full Text :
- https://doi.org/10.2478/mjpaa-2023-0020