$\mathfrak G$-bases in free (locally convex) topological vector spaces [PDF]
We characterize topological (and uniform) spaces whose free (locally convex) topological vector spaces have a local $\mathfrak G$-base. A topological space $X$ has a local $\mathfrak G$-base if every point $x$ of $X$ has a neighborhood base $(U_\alpha)_{\alpha\in\omega^\omega}$ such that $U_\beta\subset U_\alpha$ for all $\alpha\le\beta$ in $\omega ...
Тарас Банах, Arkady Leiderman
arxiv +5 more sources
Carathéodory–Fejér interpolation in locally convex topological vector spaces
AbstractWe study Carathéodory–Herglotz functions whose values are continuous operators from a locally convex topological vector space which admits the factorization property into its conjugate dual space. We show how this case can be reduced to the case of functions whose values are bounded operators from a Hilbert space into itself.
Daniel Alpay, Olga Timoshenko, Dan Volok
openalex +3 more sources
Generalized quasi-variational inequalities in locally convex topological vector spaces
AbstractLet E be a Hausdorff topological vector space and X ⊂ E an arbitrary nonempty set. Denote by E′ the dual space of E and the pairing between E′ and E by 〈w, x〉 for w ϵ E′ and x ϵ E. Given a point-to-set map S: X → 2X and a point-to-set map T: X → 2E′, the generalized quasi-variational inequality problem (GQVI) is to find a point ŷ ϵ S(ŷ) and a
Mau-Hsiang Shih, Kok-Keong Tan
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Some optimality conditions of set-valued optimization problems in locally convex topological vector spaces [PDF]
In this article, we work with set-valued optimization problems in locally convex topological vector spaces. We prove the equivalencies of some definitions of generalized convex maps introduced by Jeyakumar, Yang, Yang & Yang & Chen, as well as Zeng.
Renying Zeng
arxiv +3 more sources
Piecewise Linear Vector Optimization Problems on Locally Convex Hausdorff Topological Vector Spaces [PDF]
Piecewise linear vector optimization problems in a locally convex Hausdorff topological vector spaces setting are considered in this paper. The efficient solution set of these problems are shown to be the unions of finitely many semi-closed generalized polyhedral convex sets.
Nguyen Ngoc Luan
openalex +5 more sources
An ergodic measure on a locally convex topological vector space
AbstractThe aim of this paper is to give a way to construct a probability measure with nice ergodic properties on a locally convex topological vector space. We have two motivations; one is to give a generalization of a Gaussian measure and the other is to give an example of a probability measure with a rich kernel space.
Hiroshi Satō
openalex +3 more sources
Denjoy-type Integrals in Locally Convex Topological Vector Space
In this paper, we introduce AC* and ACG*-type properties and then, using theseconditions along with other concepts, define two Denjoy-type integrals of a function with values in a locally convex topological vector space (LCTVS). We show, among others, that these newly defined integrals are included in the SH integral, a stronger version of the Henstock
Rodolfo Maza, Sergio Rosales Canoy
openalex +4 more sources
Varieties of locally convex topological vector spaces [PDF]
Joseph Diestel+2 more
openalex +4 more sources
On embedding a compact convex set into a locally convex topological vector space [PDF]
Robert E. Jamison+2 more
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Mönch sets and fixed point theorems for multimaps in locally convex topological vector spaces [PDF]
We present a variety of fixed point theorems for multimaps having weakly closed graph. We state in turn Sadovskii, Monch and Daher type theorems which improve recent results in the literature. With this in mind, we introduce the definition of Monch-set.
Tiziana Cardinali+2 more
openalex +5 more sources