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The Uniform Boundedness Theorem in Asymmetric Normed Spaces [PDF]
Abstract and Applied Analysis, 2012 We obtain a uniform boundedness type theorem in the frame of asymmetric normed spaces. The classical result for normed spaces follows as a particular case.
C. Alegre, S. Romaguera, P. Veeramani
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Banach-Steinhaus theorem for linear relations on asymmetric normed spaces
Karpatsʹkì Matematičnì Publìkacìï, 2022 We study the continuity of linear relations defined on asymmetric normed spaces with values in normed spaces. We give some geometric charactirization of these mappings.
K. Bouadjila, A. Tallab, E. Dahia
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Compact bilinear operators on asymmetric normed spaces [PDF]
Topology and Its Applications, 2022 The paper is concerned with compact bilinear operators on asymmetric normed spaces. The study of multilinear operators on asymmetric normed spaces was initiated by Latreche and Dahia, Colloq. Math. (2020). We go further in this direction and prove a Schauder type theorem on the compactness of the adjoint of a compact bilinear operator and study the ...
Stefan Cobzaş
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Index of symmetry and topological classification of asymmetric normed spaces [PDF]
Rocky Mountain Journal of Mathematics, 2020 Let X, Y be asymmetric normed spaces and Lc(X, Y) the convex cone of all linear continuous operators from X to Y. It is known that in general, Lc(X, Y) is not a vector space.
Gonzalo Flores
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Quasi-Metric Properties of the Dual Cone of an Asymmetric Normed Space
Results in Mathematics, 2022 We obtain some quasi-metric properties of the dual cone of an asymmetric normed space. Thus, we prove that it is balanced, and hence its topology is completely regular. We also prove that it is complete in the sense of D. Doitchinov.
Carmen Alegre
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Local Antisymmetric Connectedness in Asymmetrically Normed Real Vector Spaces
Universal Journal of Mathematics and Applications, 2023 In this paper, some properties of locally antisymmetrically connected spaces which are the localized version of the antisymmetrically connected $T_0$-quasi-metric spaces constructed as the natural counterparts of connected complementary graphs, are ...
Nezakat Javanshır, Filiz Yıldız
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Compactness in asymmetric normed spaces
Topology and Its Applications, 2008 A systematic study of precompact and compact subsets on asymmetric normed linear spaces is developed, centering our attention in the case of linear lattices with an asymmetric norm.
Irène Ferrando, E A Sanchez Perez
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The weak topology in finite dimensional asymmetric normed spaces [PDF]
Topology and Its Applications, 2019 In this paper we show that, in contrast to what happens in a normed space, the weak topology of a finite dimensional asymmetric normed space is not necessarily the same as the topology of the asymmetric norm.
Carmen Alegre
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On the extension of semi-Lipschitz functions on asymmetric normed spaces
Journal of Numerical Analysis and Approximation Theory, 2005 Extension theorems for semi-Lipschitz functions and some properties of these extensions useful in approximation problems are presented. As illustration, a such problem is considered.
Costică Mustăţa
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On The Spaces of Linear Operators Acting Between Asymmetric Cone Normed Spaces
Mediterranean Journal of Mathematics, 2018 An asymmetric norm is a positive sublinear functional p on a real vector space X satisfying $$x=\theta _X$$x=θX whenever $$p(x)=p(-x)=0$$p(x)=p(-x)=0. Since the space of all lower semi-continuous linear functionals of an asymmetric normed space is not a ...
Pinar Zengin Alp +2 more
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