Dynamics of Cyclic Contractions
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866929398452584448 |
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| author | Baranwal, H. Chand, A. K. B. |
| author_facet | Baranwal, H. Chand, A. K. B. |
| contents | Cyclic contractions generalize the usual contractivities in metric spaces and $b$-MSs. In this paper, we enhance several fixed point theorems related to cyclic (i) Banach self-maps, (ii) Chatterjea contractivities, (iii) Kannan self-mappings, (iv) Ćirić and Hardy-Rogers, and (v) Reich contractions including local versions in $b$-metric spaces while also delineating the associated dynamics. Especially noteworthy is the expansion of the results concerning both fixed and periodic points, which are substantiated across a wider spectrum of ratio values for the aforementioned cyclic contractions within this class of spaces. Additionally, the convergence of Picard iterations towards the fixed point is rigorously established. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_15368 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Dynamics of Cyclic Contractions Baranwal, H. Chand, A. K. B. Dynamical Systems Cyclic contractions generalize the usual contractivities in metric spaces and $b$-MSs. In this paper, we enhance several fixed point theorems related to cyclic (i) Banach self-maps, (ii) Chatterjea contractivities, (iii) Kannan self-mappings, (iv) Ćirić and Hardy-Rogers, and (v) Reich contractions including local versions in $b$-metric spaces while also delineating the associated dynamics. Especially noteworthy is the expansion of the results concerning both fixed and periodic points, which are substantiated across a wider spectrum of ratio values for the aforementioned cyclic contractions within this class of spaces. Additionally, the convergence of Picard iterations towards the fixed point is rigorously established. |
| title | Dynamics of Cyclic Contractions |
| topic | Dynamical Systems |
| url | https://arxiv.org/abs/2406.15368 |