$\mathfrak G$-bases in free (locally convex) topological vector spaces [PDF]
arXiv, 2016 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 ...
Banakh, Taras, Leiderman, Arkady
arxiv +5 more sources
Carathéodory–Fejér interpolation in locally convex topological vector spaces
Linear Algebra and its Applications, 2009 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.
Alpay, Daniel +2 more
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Generalized quasi-variational inequalities in locally convex topological vector spaces
Journal of Mathematical Analysis and Applications, 1985 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]
arXivIn 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
An ergodic measure on a locally convex topological vector space
Journal of Functional Analysis, 1981 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
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Piecewise Linear Vector Optimization Problems on Locally Convex Hausdorff Topological Vector Spaces [PDF]
Acta Mathematica Vietnamica, 2017 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
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Denjoy-type Integrals in Locally Convex Topological Vector Space
European Journal of Pure and Applied Mathematics, 2021 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 Erodias Maza +1 more
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Varieties of locally convex topological vector spaces [PDF]
Bulletin of the American Mathematical Society, 1971 Diestel, Joseph +2 more
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On embedding a compact convex set into a locally convex topological vector space [PDF]
Pacific Journal of Mathematics, 1976 Jamison, R. E. +2 more
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Mönch sets and fixed point theorems for multimaps in locally convex topological vector spaces [PDF]
Fixed Point Theory, 2017 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.
CARDINALI, Tiziana +2 more
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