Logically Contractive Mappings: Fixed Points and Event-Indexed Rates
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866912530569363456 |
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| author | Alpay, Faruk Alpay, Taylan |
| author_facet | Alpay, Faruk Alpay, Taylan |
| contents | We introduce "logically contractive mappings" nonexpansive self-maps that contract along a subsequence of iterates and prove a fixed-point theorem that extends Banach's principle. We obtain event-indexed convergence rates and, under bounded gaps between events, explicit iteration-count rates. A worked example shows a nonexpansive map whose square is a strict contraction, and we clarify relations to Meir--Keeler and asymptotically nonexpansive mappings. We further generalize to variable-factor events and show that $\prod_k λ_k = 0$ (equivalently $\sum_k -\ln λ_k = \infty$) implies convergence. These results unify several generalized contraction phenomena and suggest new rate questions tied to event sparsity. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_07059 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Logically Contractive Mappings: Fixed Points and Event-Indexed Rates Alpay, Faruk Alpay, Taylan Functional Analysis Dynamical Systems 47H10, 47H09, 54H25 We introduce "logically contractive mappings" nonexpansive self-maps that contract along a subsequence of iterates and prove a fixed-point theorem that extends Banach's principle. We obtain event-indexed convergence rates and, under bounded gaps between events, explicit iteration-count rates. A worked example shows a nonexpansive map whose square is a strict contraction, and we clarify relations to Meir--Keeler and asymptotically nonexpansive mappings. We further generalize to variable-factor events and show that $\prod_k λ_k = 0$ (equivalently $\sum_k -\ln λ_k = \infty$) implies convergence. These results unify several generalized contraction phenomena and suggest new rate questions tied to event sparsity. |
| title | Logically Contractive Mappings: Fixed Points and Event-Indexed Rates |
| topic | Functional Analysis Dynamical Systems 47H10, 47H09, 54H25 |
| url | https://arxiv.org/abs/2508.07059 |