In this paper we show that by renorming an ordered Banach space, every cone P can be converted to a normal cone with constant K = 1 and consequently due to this approach every cone metric space is really a metric one and every theorem in metric space is valid for cone metric space automatically.

For sets given as finite intersections A = ⋂K k=1Ak the basic normal cone N(x̄;A) is given as ∑ kN(x̄;Ak), but such a result is not, in general, available for infinite intersections. A comparable characterization of N(x̄;A) is obtained here for a class of such infinite intersections.

In 2007, Long-Guang and Xian[3] replaced introduced cone metric spaces. They replaced the set of real numbers by an ordered Banach space in the definition of metric and generalized the notion of metric space. Recently, Ayse Sönemaz [5] proved a cone metric space with a normal cone, of course it has to be strongly minihedral, is paracompact. In this paper we omit the strongly minihedral of cone....

This paper provides KKT and saddle point optimality conditions, duality theorems and stability theorems for consistent convex optimization problems posed in locally convex topological vector spaces. The feasible sets of these optimization problems are formed by those elements of a given closed convex set which satisfy a (possibly in…nite) convex system. Moreover, all the involved functions are ...

In this paper, a new definition of locally convex L-topological vector spaces is given. The relationship between this new definition and the previous definition of locally convex L-topological vector spaces given by Yan and Fang in 1999 is investigated. Moreover, the concept of generalized L-fuzzy semi-norm is introduced. By using a family of generalized L-fuzzy semi-norms, a characterization o...

We characterize the existence of a nonnegative, sublinear and continuous order-preserving function for a not necessarily complete preorder on a real convex cone in an arbitrary topological real vector space. As a corollary of the main result, we present necessary and sufficient conditions for the existence of such an order-preserving function for a complete preorder.

We discuss in this paper Sche e’s method for constructing simultaneous con!dence intervals which hold for all linear combinations of the parameters subject to the weight vector being restricted to a convex cone. c © 2003 Elsevier B.V. All rights reserved.

In this paper we are concerned with the space of tempered ultrahyperfunctions corresponding to a proper open convex cone. A version of the celebrated edge of the wedge theorem will be given for this setting. As application, a version is also given of the principle of determination of an analytic function by its values on a non-empty open real set.