标题： 逻辑压缩映射：不动点和事件索引速率 显示英文标题

标题： Logically Contractive Mappings: Fixed Points and Event-Indexed Rates

摘要： 我们引入“逻辑压缩映射”即非扩张自映射，在迭代子序列上进行压缩，并证明了一个扩展巴拿赫原理的不动点定理。 我们获得了事件索引的收敛速率，并在事件之间存在有界间隔的情况下，得到了显式的迭代次数速率。 一个实际例子展示了其平方为严格压缩的非扩张映射，并澄清了与梅尔-基勒和渐近非扩张映射的关系。 我们进一步推广到可变因子事件，并表明$\prod_k \lambda_k = 0$（等价于$\sum_k -\ln \lambda_k = \infty$）意味着收敛。 这些结果统一了多种广义压缩现象，并提出了与事件稀疏性相关的新的速率问题。 显示英文摘要

摘要： 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 $\prod_k \lambda_k = 0$ (equivalently $\sum_k -\ln \lambda_k = \infty$) implies convergence. These results unify several generalized contraction phenomena and suggest new rate questions tied to event sparsity.