A Fixed Point Theorem for Random Asymptotically Pointwise Contractions
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866917453938819072 |
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| author | Shi, Jie |
| author_facet | Shi, Jie |
| contents | This paper combines the decomposition technique ($σ$-stability) in random functional analysis with the deterministic theory of asymptotically pointwise contractions to provide a complete self-contained derivation of a fixed point theorem for random asymptotically pointwise contractions. We assume the contraction function is linear $ψ(t)=λt$ ($λ<1$) and focus on the linear case under the assumption that $G$ is bounded. By choosing $p$ sufficiently large so that $5^{1/p}λ<1$, we apply the deterministic theorem in $L^p(E)$. The paper gives detailed explanations of concepts such as random normed modules, the $(ε,λ)$-topology, and $σ$-stability, and reviews the historical development of fixed point theory in the introduction. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_11228 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A Fixed Point Theorem for Random Asymptotically Pointwise Contractions Shi, Jie Functional Analysis This paper combines the decomposition technique ($σ$-stability) in random functional analysis with the deterministic theory of asymptotically pointwise contractions to provide a complete self-contained derivation of a fixed point theorem for random asymptotically pointwise contractions. We assume the contraction function is linear $ψ(t)=λt$ ($λ<1$) and focus on the linear case under the assumption that $G$ is bounded. By choosing $p$ sufficiently large so that $5^{1/p}λ<1$, we apply the deterministic theorem in $L^p(E)$. The paper gives detailed explanations of concepts such as random normed modules, the $(ε,λ)$-topology, and $σ$-stability, and reviews the historical development of fixed point theory in the introduction. |
| title | A Fixed Point Theorem for Random Asymptotically Pointwise Contractions |
| topic | Functional Analysis |
| url | https://arxiv.org/abs/2604.11228 |