标题： 正线性算子的预解式组合 显示英文标题

标题： Resolvent Compositions for Positive Linear Operators

摘要： 最近引入了预解组合，作为保持单调性的操作，将一个集值单调算子和一个有界线性算子结合起来。 它们特别推广了预解平均的概念。 我们分析当单调算子是一个严格正线性算子时的预解组合。 我们建立了几个新性质，包括 Löwner偏序关系和渐近行为。 此外，我们证明了预解组合操作在Thompson度量下是不扩展的。 我们还引入了一种新的几何插值形式，并探讨其与预解组合的联系。 最后，我们研究了基于预解组合的两个非线性方程。 显示英文摘要

摘要： Resolvent compositions were recently introduced as monotonicity-preserving operations that combine a set-valued monotone operator and a bounded linear operator. They generalize in particular the notion of a resolvent average. We analyze the resolvent compositions when the monotone operator is a strictly positive linear operator. We establish several new properties, including L\"owner partial order relations and asymptotic behavior. In addition, we show that the resolvent composition operations are nonexpansive with respect to the Thompson metric. We also introduce a new form of geometric interpolation and explore its connections to resolvent compositions. Finally, we study two nonlinear equations based on resolvent compositions.