The classical Loewner’s theorem states that operator monotone functions on real intervals are described by holomorphic the upper half-plane. We characterize local order isomorphisms domains biholomorphic automorphisms of generalized half-plane, which is collection all operators with positive invertible imaginary part. describe such maps in an explicit manner, and examine properties maximal isom...

We are concerned with the study of a class of forward-backward penalty schemes for solving variational inequalities 0 ∈ Ax+NC(x) where H is a real Hilbert space, A : H ⇉ H is a maximal monotone operator, and NC is the outward normal cone to a closed convex set C ⊂ H. Let Ψ : H → R be a convex differentiable function whose gradient is Lipschitz continuous, and which acts as a penalization functi...

We propose two inexact parallel splitting algorithms for computing the resolvent of a weighted sum of maximal monotone operators in a Hilbert space and show their strong convergence. We start by establishing new results on the asymptotic behavior of the Douglas-Rachford splitting algorithm for the sum of two operators. These results serve as a basis for the first algorithm. The second algorithm...