The aim of the present paper is to investigate the half-spaces in the convexity structure of all quasiorders on a given set and to use them in an alternative approach to classical order dimension. The main result states that linear orders can almost always be replaced by half-space quasiorders in the definition of the dimension of a partially ordered set.

For Markov chains with a finite, partially ordered state space, we show strong stationary duality under the condition of Möbius monotonicity of the chain. We give examples of dual chains in this context which have no downwards transitions. We illustrate general theory by an analysis of nonsymmetric random walks on the cube with an interpretation for unreliable networks of queues.

A decision-theoretic framework is described for sequential classification when the parameter space is a finite partially ordered set. An example of an optimal strategy is then presented. This example establishes that an asymptotically optimal class of experiment selection rules is not necessarily optimal in the given decision-theoretic setting.

Let (X, d, ) be a partially ordered metric space. Let F, G be two set valued mappings and f , g two single valued mappings on X . We obtained sufficient conditions for existence of common fixed point of F , G, f and g satisfying an implicit relation in X .

The aim of the present paper is to investigate the half-spaces in the convexity structure of all quasiorders on a given set and to use them in an alternative approach to classical order dimension. The main result states that linear orders can almost always be replaced by half-space quasiorders in the definition of the dimension of a partially ordered set.

In this study, we examine the monotone convergence of Newton-like methods to a solution of an equation on a partially ordered topological space setting. In particular we provide suucient conditions for the construction of accelerating sequences. This way the solution is obtained faster than in earlier results.

In this paper, we consider the concept of Ω-distance on a complete, partially ordered G-metric space and prove a fixed point theorem for (ψ, φ)-Weak contraction. Then, we present some applications in integral equations. c ©2013 All rights reserved.

Let H be a separable complex Hilbert space. Denote by G∞(H) the Grassmannian consisting of closed linear subspaces with infinite dimension and codimension. This Grassmannian is partially ordered by the inclusion relation. We show that every continuous order preserving bijective transformation of G∞(H) is induced by an invertible bounded semi-linear operator.

The paper presents a generalization of a known density theorem of Arrow, Barankin, and Blackwell for properly efficient points defined as support points of sets with respect to monotonically increasing sublinear functions. This result is shown to hold for nonconvex sets of a reflexive Banach space partially ordered by a Bishop–Phelps cone.