We prove that there is a bijection between the families of regular and non-regular operator monotone functions. As an application we give a new proof of the operator monotonicity of a certain class of functions related to Wigner-Yanase-Dyson skew information. 2000 Mathematics Subject Classification. Primary 62B10, 94A17; Secondary 46L30, 46L60.

In this paper we consider a proximal point algorithm (PPA) for solving the nonlinear complementarity problem (NCP) with a P 0 function. PPA was originally proposed by Martinet and further developed by Rockafellar for monotone variational inequalities and monotone operator problems. PPA is known to have nice convergence properties under mild conditions. However, until now, it has been applied ma...

Let H be a real Hilbert space, and let C be a nonempty closed convex subset of H. Let α > 0, and let A be an α-inverse strongly-monotone mapping of C into H. Let T be a generalized hybrid mapping of C into H. Let B andW be maximal monotone operators on H such that the domains of B andW are included in C. Let 0 < k < 1, and let g be a k-contraction of H into itself. Let V be a γ -strongly monoto...

We introduce the concept of monotone point-to-set field in Riemannian manifold and give a characterization, that make clear in this definition the occult geometric meaning. We will show that the sub-differential operator of a Riemannian convex function is a monotone point-to-set field. The concept of directional derivative, which appears already in other publications, plays an important role in...

The most important open problem in Monotone Operator Theory concerns the maximal monotonicity of the sum of two maximally monotone operators provided that the classical Rockafellar’s constraint qualification holds, which is called the “sum problem”. In this paper, we establish the maximal monotonicity of A+ B provided that A and B are maximally monotone operators such that domA ∩ int domB 6= ∅,...

In this paper we consider a proximal point algorithm (PPA) for solving the nonlinear complementarity problem (NCP) with a P 0 function. PPA was originally proposed by Martinet and further developed by Rockafel-lar for monotone variational inequalities and monotone operator problems. PPA is known to have nice convergence properties under mild conditions. However, until now, it has been applied m...

In this article we study graph-distance convergence of monotone operators. First, we prove a property that has been an open problem up to now: the limit of a sequence of graph-distance convergent maximal monotone operators in a Hilbert space is a maximal monotone operator. Next, we show that a sequence of maximal monotone operators converging in the same sense in a reflexive Banach space is uni...

In this paper, a new class of over-relaxed proximal point algorithms for solving nonlinear operator equations with (A,η,m)-monotonicity framework in Hilbert spaces is introduced and studied. Further, by using the generalized resolvent operator technique associated with the (A,η,m)-monotone operators, the approximation solvability of the operator equation problems and the convergence of iterativ...

In this paper, a new system of nonlinear set-valued variational inclusions involving (H, η)-monotone mappings in Hilbert spaces is introduced and studied. By using the resolvent operator method associated with (H, η)-monotone mappings, an existence theorem of solutions for this kind of system of nonlinear set-valued variational inclusion is established and a new iterative algorithm is suggested...

This technical note describes a monotone and continuous xpoint operator to compute the answer sets of programs with aggregates. The xpoint operator relies on the notion of aggregate solution. Under certain conditions, this operator behaves identically to the three-valued immediate consequence operator aggr P for aggregate programs, independently proposed in (Pelov 2004; Pelov et al. 2004). This...