We introduce a new type of the system of generalized strong vector quasiequilibrium problems with set-valued mappings in real locally convex Hausdorff topological vector spaces. We establish an existence theorem by using Kakutani-Fan-Glicksberg fixed-point theorem and discuss the closedness of strong solution set for the system of generalized strong vector quasiequilibrium problem. The results ...

Received: 27 March 2012; Accepted: 25 July 2012. Published online: XX July. 2012 Abstract: In this paper, we prove a common fixed point theorem for occasionally weakly compatible mappings on fuzzy metric space satisfying an implicit relation. Our result never requires the completeness (or closedness) of the whole space (or subspaces), containment of ranges amongst involved mappings and continui...

We study closedness properties of internal relations in finitely complete categories, which leads to developing a unified approach to: Mal’tsev categories, in the sense of A.Carboni, J. Lambek and M.C.Pedicchio, that generalize Mal’tsev varieties of universal algebras; unital categories, in the sense of D.Bourn, that generalize pointed Jónsson-Tarski varieties; and subtractive categories, intro...

In this paper we revisit the question of when the continuous linear image of a fixed closed convex cone K is closed. Specifically, we improve the main result of [3] by showing that for all, except for at most a σ-porous set, of the linear mappings T from Rn into Rm, not only is T (K) closed, but there is also a neighbourhood around T whose members also preserve the closedness of K. AMS (2002) s...

In this paper, the characterization of closed and strongly closed subobjects of an object in categories of various types of filter convergence spaces is given and it is shown that they induce a notion of closure. Furthermore, each of the notions of compactness, perfectness, separation, minimality and absolute closedness with respect to these two new closure operators are characterized in these ...

We characterize in a reflexive Banach space all the closed convex sets containing no lines for which the condition ensures the closedness of the algebraic difference for all closed convex sets . We also answer a closely related problem: determine all the pairs , of closed convex sets containing no lines such that the algebraic difference of any sufficiently small uniform perturbation of and rem...

A mixture preorder is a on space (such as convex set) that compatible with the mixing operation. In decision theoretic terms, it satisfies central expected utility axiom of strong independence. We consider when has multi-representation consists real-valued, mixture-preserving functions. If does, must satisfy continuity Herstein and Milnor (1953). Mixture sufficient for dimension countable, but ...

In many areas of applied mathematics, decentralization information is a ubiquitous attribute affecting how to approach stochastic optimization, decision and estimation, or control problem. this review article, we present general formulation structures under probability theoretic geometric formulation. We define structures, place various topologies on them, study closedness, compactness convexit...

We propose a new class of stochastic integer programs whose special features are dominance constraints induced by mixed-integer linear recourse. For these models, we establish closedness of the constraint set mapping with the underlying probability measure as parameter. In the case of finite probability spaces, the models are shown to be equivalent to large-scale, block-structured, mixedinteger...

Multi-species reaction-diffusion systems, with more-than-two-site interaction on a one-dimensional lattice are considered. Necessary and sufficient constraints on the interaction rates are obtained, that guarantee the closedness of the time evolution equation for Ea n (t)’s, the expectation value of the product of certain linear combination of the number operators on n consecutive sites at time...