Local versions of Tarski’s theorem for correspondences

Abstract

For a strong set order increasing (resp., strongly monotone) upper order hemicontinuous correspondence mapping a complete lattice A into itself (resp., a sigma-complete lattice into itself), we provide conditions for tight fixed-point bounds for sufficiently large iterations starting from any initial point in A. Our results prove a local version of the Veinott-Zhou generalization of Tarski’s theorem, as well as provide a new global version of the Tarski-Kantorovich principle for correspondences.