A generalization of irreducible monotonicity

AbstractLet K1 and K2 be pointed closed convex cones with nonempty interiors in Rn and Rm, respectively. Define A ϵ M(K1, K2) if and only if A x ϵ K2, 0 ≠ x ϵ K1, is consistent and A x ϵ K2, 0 ≠ x ϵ K1 ⇒ x ϵ intK1. If K1 and K2 are the nonnegative orthants in their respective spaces, the class M(K1, K2) reduces to the class M of irreducible matrices defined by Fiedler and Ptak [7]. Properties of matrices in M are generalized for matrices in M(K1, K2). It is shown that the irreducible MK matrices, e.g., [8], is a subset of M(K, K)