Admissible perturbations of a multivalued Picard operator: Ćirić contraction condition; fixed point and stability results
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866908621189677056 |
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| author | Gheorghe, Cristina |
| author_facet | Gheorghe, Cristina |
| contents | This paper studies strict fixed point and stability results for multivalued operators which does not satisfy a Ćirić type contraction condition, but their admissible perturbation does. We focus on the conditions imposed on the admissible perturbation $T_G$ of a Picard operator $T:X\rightarrow P(X)$ such that the strict fixed point and stability results still hold for T. The results obtained are reformulated in terms of admissible perturbations in the sense of Takahashi and illustrated with some examples. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_26896 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Admissible perturbations of a multivalued Picard operator: Ćirić contraction condition; fixed point and stability results Gheorghe, Cristina Functional Analysis 47H10, 54H25 This paper studies strict fixed point and stability results for multivalued operators which does not satisfy a Ćirić type contraction condition, but their admissible perturbation does. We focus on the conditions imposed on the admissible perturbation $T_G$ of a Picard operator $T:X\rightarrow P(X)$ such that the strict fixed point and stability results still hold for T. The results obtained are reformulated in terms of admissible perturbations in the sense of Takahashi and illustrated with some examples. |
| title | Admissible perturbations of a multivalued Picard operator: Ćirić contraction condition; fixed point and stability results |
| topic | Functional Analysis 47H10, 54H25 |
| url | https://arxiv.org/abs/2510.26896 |