Metric estimates for the calculus of multimappings
The paper contains estimates for \(d(z,E(x))\) where \(E\) is a multifunction of the form \(E(x)= F(x)\cap H^{-1} (G(x))\), and for \(d(z,F(x) \cap G(x))\). \(F\) and \(G\) are convex-valued and \(H\) a convex multifunction, acting between normed linear spaces. Then some consequences about continuity properties of multifunctions obtained via intersections or inverse images are deduced, also whithout convexity assumptions. Applications to the differential calculus of multifunctions as well as to the calculus of normal cones are finally provided.
scientific article; zbMATH DE number 1145867