  Recently, Liu, Moursi and Vanderwerff have introduced the class of super
strongly nonexpansive mappings as a counterpart to operators which are
maximally monotone and uniformly monotone. We give a quantitative study of
these notions in the style of proof mining, providing a modulus of super strong
nonexpansiveness, giving concrete examples of it and connecting it to moduli
associated to uniform monotonicity. For the supercoercive case, we analyze the
situation further, yielding a quantitative inconsistent feasibility result for
this class (obtaining effective uniform rates of asymptotic regularity), a
result which is also qualitatively new.
