  Starting from a characterization of holomorphic functions in terms of a
suitable mean value property, we build some nonlinear asymptotic
characterizations for complex-valued solutions of certain nonlinear systems,
which have to do with the classical Cauchy-Riemann equations. From these
asymptotic characterizations, we derive suitable asymptotic mean value
properties, which are used to construct appropriate vectorial dynamical
programming principles. The aim is to construct approximation schemes for the
so-called contact solutions, recently introduced by N. Katzourakis, of the
nonlinear systems here considered.
