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| Natura: | Preprint |
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2025
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| Accesso online: | https://arxiv.org/abs/2503.00207 |
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| _version_ | 1866916636347334656 |
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| author | Gheorghe, Cristina Petruşel, Adrian |
| author_facet | Gheorghe, Cristina Petruşel, Adrian |
| contents | The aim of this paper is to give strict fixed point principles for multivalued operators $T:X\rightarrow P(X)$ satisfying some contraction conditions of Ćiri\' c and of Ćiri\' c-Reich-Rus type. We are interested, under which conditions, the multi-valued operator has a unique strict fixed point and, additionally, when the sequence of its multi-valued iterates $(T^n(x))_{n\in \mathbb{N}}$ converges to this unique strict fixed point. Moreover, some stability properties, such as data dependence on operator perturbation, Ulam-Hyers stability, well-posedness in the sense of Reich and Zaslavski and Ostrowski property of the strict fixed point problem are established. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_00207 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Strict fixed point problem, stability results and retraction displacement condition for Picard operators Gheorghe, Cristina Petruşel, Adrian Functional Analysis 47H10, 54H25 The aim of this paper is to give strict fixed point principles for multivalued operators $T:X\rightarrow P(X)$ satisfying some contraction conditions of Ćiri\' c and of Ćiri\' c-Reich-Rus type. We are interested, under which conditions, the multi-valued operator has a unique strict fixed point and, additionally, when the sequence of its multi-valued iterates $(T^n(x))_{n\in \mathbb{N}}$ converges to this unique strict fixed point. Moreover, some stability properties, such as data dependence on operator perturbation, Ulam-Hyers stability, well-posedness in the sense of Reich and Zaslavski and Ostrowski property of the strict fixed point problem are established. |
| title | Strict fixed point problem, stability results and retraction displacement condition for Picard operators |
| topic | Functional Analysis 47H10, 54H25 |
| url | https://arxiv.org/abs/2503.00207 |