Locally convex topological vector space
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On the embedding of convex spaces in stratified L-convex spaces Open
Consider L being a continuous lattice, two functors from the category of convex spaces (denoted by CS) to the category of stratified L-convex spaces (denoted by SL-CS) are defined. The first functor enables us to prove that the category CS…
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The Bishop-Phelps-Bollobas property for operators between spaces of continuous functions Open
We show that the space of bounded linear operators between spaces of continuous functions on compact Hausdorff topological spaces has the Bishop-Phelps-Bollobas property. A similar result is also proved for the class of compact operators f…
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Inertial forward–backward methods for solving vector optimization problems Open
We propose two forward-backward proximal point type algorithms with inertial/memory effects for determining weakly efficient solutions to a vector optimization problem consisting in vector-minimizing with respect to a given closed convex p…
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Fixed point theorems in r-normed and locally r-convex spaces and applications Open
In this paper we prove some new fixed point theorems in r-normed and locally r-convex spaces.Our conclusions generalize many well-known results and provide a partial affirmative answer to Schauder's conjecture.Based on the obtained results…
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Dynamics of weighted composition operators on function spaces defined by local properties Open
We study topological transitivity/hypercyclicity and topological (weak) mixing for weighted composition operators on locally convex spaces of scalar-valued functions which are defined by local properties. As main application of our general…
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Convergence structures in (L,M)-fuzzy convex spaces Open
This paper presents the concepts of (L,M)-remotehood spaces and (L,M)-convergence spaces in the framework of (L,M)-fuzzy convex spaces. Firstly, it is shown that the category of (L,M)-remotehood spaces is isomorphic to the category of (L,M…
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(L,M)-fuzzy topological-convex spaces Open
In this paper, the notion of (L,M)-fuzzy topological-convex spaces is introduced and some of its characterizations are obtained. Then the notion of (L,M)-fuzzy convex enclosed relation spaces is introduced and its one-to-one correspondence…
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Fans and their applications in General Topology, Functional Analysis and Topological Algebra Open
A family of closed subsets of a topological space $X$ is called a (strict) $Cld$-fan in $X$ if this family is (strictly) compact-finite but not locally finite in $X$. Applications of (strict) $Cld$-fans are based on a simple observation th…
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α-Topological Vector Spaces Open
The main objective of this paper is to present the study of α-topological vector spaces. α-topological vector spaces are defined by using α-open sets and α-irresolute mappings. Notions of convex, balanced and bounded set are introduced and…
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A categorical approach to abstract convex spaces and interval spaces Open
In this paper, we establish the axiomatic conditions of hull operators and introduce the category of interval spaces. We also investigate their relations with convex spaces from a categorical sense. It is shown that the category CS of conv…
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Open source vector field topology Open
A myriad of physical phenomena, such as fluid flows, magnetic fields, and population dynamics are described by vector fields. More often than not, vector fields are complex and their analysis is challenging. Vector field topology is a powe…
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Tree algebras over topological vector spaces in rough path theory Open
We work with non-planar rooted trees which have a label set given by an arbitrary vector space $V$. By equipping $V$ with a complete locally convex topology, we show how a natural topology is induced on the tree algebra over $V$. In this c…
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On free locally convex spaces Open
Let L(X) be the free locally convex space over a Tychonoff space X. We prove that the following assertions are equivalent: (i) every functionally bounded subset of X is finite, (ii) L(X) is semi-reflexive, (iii) L(X) has the Grothendieck p…
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On Irresolute Topological Vector Spaces Open
In this paper, our focus is to investigate the notion of irresolute topological vector spaces. Irresolute topological vector spaces are defined by using semi open sets and irresolute mappings. The notion of irresolute topological vector sp…
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Continuity of approximate solution maps to vector equilibrium problems Open
This paper considers the parametric primal and dual vector equilibrium problems in locally convex Hausdorff topological vector spaces. Based on linear scalarization technique, we establish sufficient conditions for the continuity of approx…
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Regularity in Topological Modules Open
The framework of Functional Analysis is the theory of topological vector spaces over the real or complex field. The natural generalization of these objects are the topological modules over topological rings. Weakening the classical Functio…
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Nano ∆ generalized-closed sets in nano topological spaces Open
In this paper, we study the schauder-tychonoff fixed point (STFP) on a subset A of a sequentially complete Hausdorff strongly convex topological vector space (SCHSCTVS) E (over the field R) with calibration Γ have a unique STFP in Topologi…
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Non-Linear Inner Structure of Topological Vector Spaces Open
Inner structure appeared in the literature of topological vector spaces as a tool to characterize the extremal structure of convex sets. For instance, in recent years, inner structure has been used to provide a solution to The Faceless Pro…
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When is there a representer theorem? Open
We consider a general regularised interpolation problem for learning a parameter vector from data. The well known representer theorem says that under certain conditions on the regulariser there exists a solution in the linear span of the d…
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On generalized approximate convex functions and variational inequalities Open
In this paper, we consider a vector optimization problem involving locally Lipschitz generalized approximately convex functions and provide several concepts of approximate efficient solutions. We formulate approximate vector variational in…
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Are All Good Word Vector Spaces Isomorphic? Open
Existing algorithms for aligning cross-lingual word vector spaces assume that vector spaces are approximately isomorphic. As a result, they perform poorly or fail completely on non-isomorphic spaces. Such non-isomorphism has been hypothesi…
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On almost \(s-\)topological vector spaces Open
In this paper, we introduce the notion of almost \(s-\)topological vector spaces and present some examples and counterexamples of almost \(s-\)topological vector spaces. Some general properties of almost \(s-\)topological vector spaces are…
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Some general fixed point theorems on topological vector spaces Open
In this paper, we introduce some of general fixed point theorems on topological vector spaces.The first one is a general theorem for the better admissible multimaps and the second one for generalized upper hemicontinuous (g.u.h.c.) convex-…
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The Josefson-Nissenzweig property for locally convex spaces Open
We define a locally convex space E to have the Josefson-Nissenzweig property (JNP) if the identity map (E?, ?(E?, E)) ? (E?, ?*(E?, E)) is not sequentially continuous. By the classical Josefson-Nissenzweig theorem, every infinite-dimension…
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Mönch sets and fixed point theorems for multimaps in locally convex topological vector spaces Open
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…
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Approximate weakly efficient solutions of set-valued vector equilibrium problems Open
In this paper, we introduce a new kind of approximate weakly efficient solutions to the set-valued vector equilibrium problems with constraints in locally convex Hausdorff topological vector spaces; then we discuss a relationship between t…
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Degenerate multi-term fractional differential equations in locally convex spaces Open
We investigate, in the setting of sequentially complete locally convex spaces, degenerate multi-term fractional differential equations with Caputo derivatives. The obtained theoretical results are illustrated with some examples.
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Neutrosophic Quadruple Vector Spaces and Their Properties Open
In this paper authors for the first time introduce the concept of Neutrosophic Quadruple (NQ) vector spaces and Neutrosophic Quadruple linear algebras and study their properties. Most of the properties of vector spaces are true in case of …
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Multivariate contraction mapping principle with the error estimate formulas in locally convex topological vector spaces and application Open
The purpose of this paper is to present the concept of multivariate contraction mapping in a locally convex topological vector spaces and to prove the multivariate contraction mapping principle in such spaces.The neighborhood-type error es…
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Algebras of the Extended Probabilistic Powerdomain Monad Open
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