Quasi-complete, locally convex topological vector spaces V have the useful property that continuous compactly-supported V -valued functions have integrals with respect to finite Borel measures. Rather than constructing integrals as limits following [Bochner 1935], [Birkhoff 1935], et alia, we use the [Gelfand 1936][Pettis 1938] characterization of integrals, which has good functorial properties...

We construct a denotational model of linear logic, whose objects are all the locally convex and separated topological vector spaces endowed with their weak topology. The negation is interpreted as the dual, linear proofs are interpreted as continuous linear functions, and non-linear proofs as sequences of monomials. We do not complete our constructions by a double-orthogonality operation. This ...

In this paper, the authors prove some existence results of solutions for a new class of generalized quasi-variational inequalities (GQVI) for pseudo-monotone type III operators and strongly pseudo-monotone type III operators defined on noncompact sets in locally convex Hausdorff topological vector spaces. In obtaining these results on GQVI for pseudo-monotone type III operators, we shall use Ch...

We show that there are two (isomorphic) full subcategories of the category of locally convex topological vector spaces—the weakly topologized spaces and those with the Mackey topology—that form ∗-autonomous categories. RÉSUMÉ. On montre qu’il y a deux sous-catégories (isomorphes) pleines de la catégorie des espaces vectoriels topologiques localement convexes—les espaces munis de la topologie fa...

We prove some existence results of solutions for a new class of generalized bi-quasivariational inequalities GBQVI for quasi-pseudomonotone type II and strongly quasi-pseudomonotone type II operators defined on noncompact sets in locally convex Hausdorff topological vector spaces. To obtain these results on GBQVI for quasi-pseudomonotone type II and strongly quasipseudomonotone type II operator...

We consider the DC optimization problem (P) inf x∈X {(f1(x) − f2(x)) + (g1(Ax) − g2(Ax))}, where f1, f2, g1 and g2 are proper convex functions defined on locally convex Hausdorff topological vector spaces X and Y respectively, and A is a linear continuous operator from X to Y . Adopting the standard convexification technique, a Fenchel dual problem of (P) is given. By using properties of the ep...

This is to recollect the equivalent formulations of Brouwer fixed point theorem. We collect a large number recently known sources such equivalents. More recently, Jinlu Li obtained two theorems on newly defined quasi-point-separable topological vector spaces. His extend Tychonoff theorem locally convex t.v.s. However, we note that his new are logically Consequently, add up our list

In this paper, we first consider the class of minimal time functions in general setting locally convex topological vector (LCTV) spaces. The results obtained framework are based on a novel notion closedness target sets with respect to constant dynamics. Then, introduce and investigate new signed functions, which generalizations distance functions. Subdifferential formulas for under convexity as...

We develop a theory for sensitivity with respect to parameters in a convex subset of a topological vector space of dynamical systems in a Banach space. Specific motivating examples for probability measure dependent differential, partial differential and delay differential equations are given. Schemes that approximate the measures in the Prohorov sense are illustrated with numerical simulations ...