Results 1 to 10 of about 191 (93)

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 \
García-Raffi, L.M., Romaguera, S., Sánchez-Pérez, E.A.   +2 more
exaly   +4 more sources

Extension of bounded linear functionals and best approximation in spaces with asymmetric norm

Journal of Numerical Analysis and Approximation Theory, 2004
The present paper is concerned with the characterization of the elements of best approximation in a subspace \(Y\) of a space with asymmetric norm, in terms of some linear functionals vanishing on \(Y\).
Ş. Cobzaş, C. Mustăţa
doaj   +6 more sources

On the uniqueness of extension and unique best approximation in the dual of an asymmetric normed linear space

Journal of Numerical Analysis and Approximation Theory, 2003
A well known result of R. R. Phelps (1960) asserts that in order that every linear continuous functional, defined on a subspace \(Y\) of a real normed space \(X\), have a unique norm preserving extension it is necessary and sufficient that its ...
Costică Mustăţa
doaj   +6 more sources

Compactness and finite dimension in asymmetric normed linear spaces

Topology and its Applications, 2005
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
L M Garcia-Raffi
exaly   +5 more sources

Asymmetric norms and optimal distance points in linear spaces

Topology and its Applications, 2008
Let \(X\) be a real vector space. A mapping \(q : X \to [0, \infty)\) is called an asymmetric norm and \((X,q)\) an asymmetric normed space if it satisfies, for all \(x,y \in X\) and \(a \geq 0\), the conditions \(q(a x) = a q(x),\; q(x+y) \leq q(x) + q(y)\), and \(q(x) = q(-x) = 0\) only for \(x = 0\).
García Raffi, L.M., Sánchez Pérez, E.A.   +1 more
openaire   +3 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.
Olela Otafudu, Olivier
openaire   +4 more sources

Closedness of bounded convex sets of asymmetric normed linear spaces and the Hausdorff quasi-metric

Bulletin of the Belgian Mathematical Society - Simon Stevin, 2006
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Rodríguez-López, Jesús, Romaguera, Salvador   +1 more
openaire   +5 more sources

Banach-Steinhaus theorem for linear relations on asymmetric normed spaces

Carpathian Mathematical Publications, 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. As an application, we prove the Banach-Steinhaus theorem in the framework of asymmetric normed spaces.
K. Bouadjila, A. Tallab, E. Dahia
openaire   +2 more sources

Bipolar Theorem and Some of Its Applications in Fuzzy Quasi-Normed Space

Journal of Mathematics
The classical bipolar theorem plays an important role in functional analysis. This paper generalizes this theorem to fuzzy quasi-normed spaces, which include asymmetric normed space and fuzzy normed space as special cases.
Jianrong Wu, Lei Hua, Zhenyu Jin
doaj   +1 more source

Bishop-Phelps Theorem for Normed Cones

پژوهش‌های ریاضی, 2019
Introduction In the last few years there is a growing interest in the theory of quasi-metric spaces and other related structures such as quasi-normed cones and asymmetric normed linear spaces, because such a theory provides an important tool in the study
Ildar Sadeghi, Ali Hassanzadeh
doaj