Fixed Point Theorems for Multivalued Weak Contractions in Cone Metric Spaces
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866908484795105280 |
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| author | Rada, Elvin |
| author_facet | Rada, Elvin |
| contents | This article presents a deep investigation of fixed points for multivalued weak contractions in cone metric spaces. We extend Berinde weak contraction principles to the multivalued setting in cone metric spaces, developing existence, uniqueness, and convergence results. Using the structure of normal cones in Banach spaces, we prove generalized fixed-point theorems for set-valued mappings satisfying weak contractive conditions. The theoretical framework includes iterative approximation schemes with explicit convergence rates and stability analysis of fixed point sets. In the end, some applications to differential inclusions and variational inequalities demonstrate the utility of our results in nonlinear analysis. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_08261 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Fixed Point Theorems for Multivalued Weak Contractions in Cone Metric Spaces Rada, Elvin Functional Analysis 47H10, 47H04 This article presents a deep investigation of fixed points for multivalued weak contractions in cone metric spaces. We extend Berinde weak contraction principles to the multivalued setting in cone metric spaces, developing existence, uniqueness, and convergence results. Using the structure of normal cones in Banach spaces, we prove generalized fixed-point theorems for set-valued mappings satisfying weak contractive conditions. The theoretical framework includes iterative approximation schemes with explicit convergence rates and stability analysis of fixed point sets. In the end, some applications to differential inclusions and variational inequalities demonstrate the utility of our results in nonlinear analysis. |
| title | Fixed Point Theorems for Multivalued Weak Contractions in Cone Metric Spaces |
| topic | Functional Analysis 47H10, 47H04 |
| url | https://arxiv.org/abs/2508.08261 |