We prove that every element of the polar cone to the closed convex cone of monotone transport maps can be represented as the divergence of a measure field taking values in the positive definite matrices.

In the present paper, we extend known KKM theorems and matching theorems for generalized KKM maps to G-convex spaces. From these results, we deduce generalized versions of main results of Kassay and Kolumbán [KK] and some others.

In this paper, a Krein-Milman  type theorem in $T_0$ semitopological cone is proved,  in general. In fact, it is shown that in any locally convex $T_0$ semitopological cone, every convex compact saturated subset is the compact saturated convex hull of its extreme points, which improves the results of Larrecq.

The aim of this paper is to show that under a mild semicontinuity assumption (the so-called segmentary epi-closedness), the cone-convex (resp. cone-quasiconvex) set-valued maps can be characterized in terms of weak cone-convexity (resp. weak cone-quasiconvexity), i.e. the notions obtained by replacing in the classical definitions the conditions of type ”for all x, y in the domain and for all t ...

metric spaces and approximating fixed points of a pair of contractive type mappings M. Abbas, M. Jovanović, S. Radenović University of Belgrade School of Electrical Engineering http://www.etf.bg.ac.rs JOURNAL OF COMPUTATIONAL ANALYSIS AND APPLICATIONS, Vol. 13, No. 2, pp. 243253, Jan, 2011 References: Abstract: Recently, Chao Wang, Jinghao Zhu, Boško Damjanović, Liang-gen Hu [Approximating fixe...

In this paper, we define the almost uniform convergence and the almost everywhere convergence for cone-valued functions with respect to an operator valued measure. We prove the Egoroff theorem for Pvalued functions and operator valued measure θ : R → L(P, Q), where R is a σ-ring of subsets of X≠ ∅, (P, V) is a quasi-full locally convex cone and (Q, W) is a locally ...

Let Ln be the n-dimensional second order cone. A linear map from R m to Rn is called positive if the image of Lm under this map is contained in Ln. For any pair (n, m) of dimensions, the set of positive maps forms a convex cone. We construct a linear matrix inequality of size (n−1)(m−1) that describes this cone.

It has been shown by Lemke that if a matrix is copositive plus on IR n , then feasibility of the corresponding Linear Complementarity Problem implies solvability. In this article we show, under suitable conditions, that feasibility of a Generalized Linear Complementarity Problem (i.e., deened over a more general closed convex cone in a real Hilbert Space) implies solvability whenever the operat...

The well-known result stating that any non-convex quadratic problem over the nonnegative orthant with some additional linear and binary constraints can be rewritten as linear problem over the cone of completely positive matrices (Burer, 2009) is generalized by replacing the nonnegative orthant with an arbitrary closed convex cone. This set-semidefinite representation result implies new semidefi...