Resolvents of set-valued operators play a central role in various branches of mathematics and in particular in the design and the analysis of splitting algorithms for solving monotone inclusions. We propose a generalization of this notion, called warped resolvent, which is constructed with the help of an auxiliary operator. The properties of warped resolvents are investigated and connections are made with existing notions. Abstract weak and strong convergence principles based on warped resolvents are proposed and shown to not only provide a synthetic view of splitting algorithms but to also constitute an effective device to produce new solution methods for challenging inclusion problems.

中文翻译：

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单调内含物的扭曲近端迭代

集值算子的求解在数学的各个分支中都起着核心作用，特别是在用于解决单调包含的分裂算法的设计和分析中。我们提出了这个概念的概括，称为扭曲解析，它是在辅助算子的帮助下构建的。研究了扭曲的解决方案的特性，并与现有概念建立了联系。提出了基于扭曲求解器的抽象弱收敛和强收敛原理，并表明它们不仅提供了分裂算法的综合视图，而且还构成了一种有效的设备，可以为具有挑战性的包含问题产生新的解决方法。