Compactness in probabilistic Hilbert space

Reproducing kernel Hilbert space semantics for probabilistic programs

We propose denotational semantics for a language of probabilistic arithmetic expressions based on reproducing kernel Hilbert spaces (RKHS). The RKHS approach has numerous practical advantages, but from a semantics point of view the most important is ability to provide convergence guarantees on approximate evaluations of expressions. We present preliminary results on convergence bounds, adapting...

Menger probabilistic normed space is a category topological vector space

In this paper, we formalize the Menger probabilistic normed space as a category in which its objects are the Menger probabilistic normed spaces and its morphisms are fuzzy continuous operators. Then, we show that the category of probabilistic normed spaces is isomorphicly a subcategory of the category of topological vector spaces. So, we can easily apply the results of topological vector spaces...

Viscosity approximation methods for W-mappings in Hilbert space

We suggest a explicit viscosity iterative algorithm for nding a common elementof the set of common xed points for W-mappings which solves somevariational inequality. Also, we prove a strong convergence theorem with somecontrol conditions. Finally, we apply our results to solve the equilibrium problems.Finally, examples and numerical results are also given.

Linking in Hilbert Space

We present the most general definition of the linking of sets in a Hilbert space and, drawing on the theory given in [ST, T, Sc3], give a necessary and sufficient geometric condition for linking when one set is compact.

Lawson-compactness for the Probabilistic Powerdomain