Some fixed point results with the vector degree of nondensifiability in generalized Banach spaces and application on coupled Caputo fractional delay differential equations
In this work, we prove some fixed point results in generalized Banach spaces (GBS{\mathfrak{G}}{\mathfrak{B}}{\mathfrak{S}}s) in the sense of Perov using the vector degree of nondensifiability tools. The given result generalizes Darbo’s and Krasnoselskii’s theorems, which are connected with the vect...
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| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
| Published: |
De Gruyter
2025-01-01
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| Series: | Demonstratio Mathematica |
| Subjects: | |
| Online Access: | https://doi.org/10.1515/dema-2024-0058 |
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| Summary: | In this work, we prove some fixed point results in generalized Banach spaces (GBS{\mathfrak{G}}{\mathfrak{B}}{\mathfrak{S}}s) in the sense of Perov using the vector degree of nondensifiability tools. The given result generalizes Darbo’s and Krasnoselskii’s theorems, which are connected with the vector measure of noncompactness. An existence result for coupled Caputo fractional delay differential equations in the GBSC([−τ,T],R)×C([−τ,T],R){\mathfrak{G}}{\mathfrak{B}}{\mathfrak{S}}\hspace{0.33em}{\mathcal{C}}\left(\left[-\tau ,T],{\mathbb{R}})\times {\mathcal{C}}\left(\left[-\tau ,T],{\mathbb{R}}) is given to show the significance and the applicability of our theoretical results. |
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| ISSN: | 2391-4661 |