Characterizations of Stable Functions on L-dom ains

In this paper,the author studies the characteristic properties of stable functions between L domains. A basic notion of stable open subsets of L domain is introduced. The author shows that the two element L domains θ={0,1} is the classifier of the category of L domains and stable functions.

The Stable Farkas Lemma for Composite Convex Functions in Infinite Dimensional Spaces

In this paper, we consider a general composite convex optimization problem with a cone-convex system in locally convex Hausdorff topological vector spaces. Some Fenchel conjugate transforms for the composite convex functions are derived to obtain the equivalent condition of the Stable Farkas Lemma, which is formulated by using the epigraph of the conjugates for the convex functions involved and turns out to be weaker than the classic Slater condition. Moreover, we get some necessary and sufficient conditions for stable duality results of the composite convex functions and present an example to illustrate that the monotonic increasing property of the outer convex function in the objective function is essential. Our main results in this paper develop some recently results.

ALMOST SURE CONVERGENCE OF THE STABLE TAIL EMPIRICAL DEPENDENCE FUNCTION IN MULTIVARIATE EXTREME STATISTICS

In this paper we prove the almost sure convergence of the stable tail empirical dependence function for multivariate extreme values.

Fixed points of Scott continuous self-maps

In this paper we study the properties of the set consisting of all fixed points of a Scott continuous self-map between domains. All the results give an answer to an open problem posed by Lawson and Mislove in 1990.