Invariance of Domain for Operators of Class AG(S+)

Abstract

Let X be a real reflexive Banach space and X^∗ its dual space. Let T : X ⊃ D(T) → 2^X∗ An operator of class A_G(S₊), where G ⊂ X is open. An invariance of domain result for T is established. This result extends a similar result of Park for single-valued operators of type (S₊). The Skrypnik’s topological degree theory is used, utilizing approximating schemes of mappings of class A_G(S₊), along with the methodology of a recent invariance of domain result by Kartsatos and the author.