Andrei Sipoş
University of Bucharest & Simion Stoilow Institute of Mathematics of the Romanian Academy, Bucharest, Romania

Strongly nonexpansive mappings are a core concept in convex optimization. Recently, they have begun to be studied from a quantitative viewpoint: U. Kohlenbach has identified the notion of a modulus of strong nonexpansiveness, which leads to computational interpretations of the main results involving this class of mappings. This forms part of the greater research program of 'proof mining', initiated by G. Kreisel and highly developed by U. Kohlenbach and his collaborators, which aims to apply proof-theoretic tools to extract computational content from ordinary proofs in mainstream mathematics. The quantitative study of strongly nonexpansive mappings has later led to finding rates of asymptotic regularity for the problem of inconsistent feasibility, where one essential ingredient has been a computational counterpart of the concept of rectangularity. Last year, Liu, Moursi and Vanderwerff have introduced the class of super strongly nonexpansive mappings, and have shown that this class is tightly linked to that of uniformly monotone operators.

What we do is to provide a modulus of super strong nonexpansiveness, give examples of it in the cases e.g. averaged mappings and contractions for large distances and connect it to the modulus of uniform monotonicity. In the case where the modulus is supercoercive, we give a refined analysis, identifying a second modulus for supercoercivity, specifying the necessary computational connections and generalizing quantitative inconsistent feasibility.