Accretive and monotone operator theory are central branches of nonlinear functional analysis and constitute the abstract study of certain set-valued mappings between function spaces. This paper deals with the computational properties of these accretive and (generalized) monotone set-valued operators. In particular, we develop (and extend) for this field the theoretical framework of proof mining, a program in mathematical logic that seeks to extract computational information from prima facie “non-computational” proofs from the mainstream literature. To this end, we establish logical metatheorems that guarantee and quantify the computational content of theorems pertaining to accretive and (generalized) monotone set-valued operators. On the one hand, our results unify a number of recent case studies, while they also provide characterizations of central analytical notions in terms of proof theoretic ones on the other, which provides a crucial perspective on needed quantitative assumptions in future applications of proof mining to these branches.

增生和单调算子理论是非线性泛函分析的核心分支，构成了函数空间之间某些集值映射的抽象研究。本文讨论了这些增生和（广义）单调集值运算符的计算特性。特别是，我们为该领域开发（并扩展）证明挖掘的理论框架，这是一个数理逻辑程序，旨在从主流文献的初步“非计算”证明中提取计算信息。为此，我们建立了逻辑元定理，以保证和量化与增生和（广义）单调集值运算符有关的定理的计算内容。一方面，我们的结果统一了一些最近的案例研究，