On sum of monotone operator of type (FPV) and a maximal monotone operator

Abstract

Abstract:In the setting of a general real Banach space, we prove that the sum of a monotone operator A of type (FPV) and a maximal monotone operator B is maximal with domA ∩ int domB = φ and either domB is open or for any x ∈ domA ∩ int domB, x * ≤ |B(x)|, x * ∈ A(x).