Approximate proximal point algorithms for finding zeroes of maximal monotone operators in Hilbert spaces.
Approximate weak invariance for semilinear differential inclusions in Banach spaces
In this paper we give a criterion for a given set K in Banach space to be approximately weakly invariant with respect to the differential inclusion x′(t) ∈ Ax(t) + F(x(t)), where A generates a C 0-semigroup and F is a given multi-function, using the concept of a tangent set to another set. As an application, we establish the relation between approximate solutions to the considered differential inclusion and solutions to the relaxed one, i.e., x′(t) ∈ Ax(t) + F(x(t)), without any Lipschitz conditions...
Approximation of set-valued functions by single-valued one