Results 11 to 20 of about 1,619,215 (233)
Compactness and finite dimension in asymmetric normed linear spaces
Topology and Its Applications, 2005 We describe the compact sets of any asymmetric normed linear space. After that, we focus our attention in finite dimensional asymmetric normed linear spaces. In this case we establish the equivalence between T 1 separation axiom and normable spaces.
L. M. García-Raffi
exaly +4 more sources
Extremal function pairs in asymmetric normed linear spaces
Topology and Its Applications, 2014 This is a continuation of the previous joint paper by the author, \textit{E. Kemajou} et al. [Topology Appl. 159, No. 9, 2463--2475 (2012; Zbl 1245.54023)] on hyperconvexity on \(T_0\)-quasi-metric spaces. Sample results: Every point in the \(q\)-hyperconvex hull of an asymmertic normed linear space is extremal.
Olivier Olela Otafudu
exaly +5 more sources
TOPOLOGY OF QUASI-PSEUDOMETRIC SPACES AND CONTINUOUS LINEAR OPERATOR ON ASYMMETRIC NORMED SPACES
Journal of Fundamental Mathematics and Applications (JFMA), 2023 . In this paper, we will discuss about topological properties of quasi-pseudometric spaces and properties of linear operators in asymmetric normed spaces. The topological properties of quasi-pseudometric spaces will be given consisting of open and closed
Klatenia Selawati, C. R. Indrati
semanticscholar +2 more sources
Separation axioms and covering dimension of asymmetric normed spaces [PDF]
Quaestiones Mathematicae, 2018 It is well known that every asymmetric normed space is a T0 paratopological group. Since all Ti axioms (i = 0, 1, 2, 3) are pairwise non-equivalent in the class of paratopological groups, it is natural to ask if some of these axioms are equivalent in the
Victor Donju'an, Natalia Jonard-P'erez
semanticscholar +5 more sources
Asymmetric Normed Baire Space [PDF]
Results in Mathematics, 2021 We prove that an asymmetric normed space is never a Baire space if the topology induced by the asymmetric norm is not equivalent to the topology of a norm. More precisely, we show that a biBanach asymmetric normed space is a Baire space if and only if it is isomorphic to its associated normed space.
exaly +3 more sources
Local compactness in right bounded asymmetric normed spaces [PDF]
Quaestiones Mathematicae, 2017 We characterize the finite dimensional asymmetric normed spaces which are right bounded and the relation of this property with the natural compactness properties of the unit ball, such as compactness and strong compactness.
Natalia Jonard-P'erez +1 more
semanticscholar +6 more sources
Abstract and Applied Analysis, 2014 Asymmetric normed semilinear spaces are studied. A description of biBanach, left K-sequentially complete, and Smyth complete asymmetric normed semilinear spaces is provided and three appropriate notions of absolute convergence in the asymmetric normed ...
N. Shahzad, O. Valero
doaj +2 more sources
The Goldstine Theorem for asymmetric normed linear spaces
Topology and Its Applications, 2009 If \(X\) is a linear space, then a function \(q: X\to\mathbb{R}^+\) is called an asymmetric norm on \(X\) if for all \(x,y\in X\) and \(r\in \mathbb{R}^+\), \(x= 0\) if and only if \(q(x)= q(-x)= 0\), \(q(rx)= rq(x)\) and \(q(x+ y)= q(x)+ q(y)\). It follows that the function \(q^s: X\to\mathbb{R}\) defined by \(d^s(x)= \max(q(x), q(-x))\) is a norm on \
S Romaguera, E A Sanchez-Perez
exaly +2 more sources
Journal of MathematicsThis paper investigates the Hyers–Ulam stability of a class of generalized biquadratic functional equations involving four unknown mappings in non-Archimedean normed spaces. We analyze a coupled system that simultaneously incorporates additive, quadratic,
Janyarak Tongsomporn +1 more
doaj +2 more sources
Elementary approach to closed billiard trajectories in asymmetric normed spaces [PDF]
Proceedings of the American Mathematical Society, 2014 We apply the technique of K\'aroly Bezdek and Daniel Bezdek to study billiard trajectories in convex bodies, when the length is measured with a (possibly asymmetric) norm.
A. Akopyan +3 more
semanticscholar +5 more sources