| Autor: |
Taoudi Mohamed Aziz |
| Jazyk: |
angličtina |
| Rok vydání: |
2023 |
| Předmět: |
|
| Zdroj: |
Moroccan Journal of Pure and Applied Analysis, Vol 9, Iss 3, Pp 304-310 (2023) |
| Druh dokumentu: |
article |
| ISSN: |
2351-8227 |
| DOI: |
10.2478/mjpaa-2023-0020 |
| Popis: |
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. |
| Databáze: |
Directory of Open Access Journals |
| Externí odkaz: |
|
