  Accretive and monotone operator theory are central branches of nonlinear
functional analysis and constitute the abstract study of set-valued mappings
between function spaces. This paper deals with the computational properties of
certain large classes of operators, namely accretive and (generalized) monotone
set-valued ones. 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 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.
