Abstract
The celebrated Lax’ principle “stability and consistency implies convergence” is adapted to the case of nonlinear equation and even inclusions (multivalued equations) through a convenient concept of stability. It requires the definition of “contingent derivative” of single or set-valued maps and states that a family of maps is stable if and only if the inverses of their contingent derivatives are bounded.An extension of the Banach-Steinhauss theorem to the set-valued analogues of continuous linear operators is also provided, as well as relations between pointwise and graph convergence of sequences of set-valued maps.
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