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Continuous operators on asymmetric normed spaces
Acta Mathematica Hungarica, 2008For a real linear space, a function \(p:X\to \mathbb R^+\) is called an asymmetric norm on \(X\) if for all \(x,y\in X\) and \(r\in \mathbb R^+\), (i) \(p(x)=p(-x)=0\); (ii) \(p(rx)=rp(x)\); (iii) \(p(x+y)\leq p(x)+p(y)\). For an asymmetric norm \(p\) on \(X\), \(p^{-1}\), defined on \(X\) by \(p^{-1}(x)=p(-x)\) is also an asymmetric norm on \(X\); the
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Extensions of asymmetric norms to linear spaces
2011Summary: Let \(M\) be a subset of a (real) linear space that is closed with respect to the sum of vectors and the product by nonnegative scalars. An asymmetric seminorm on \(M\) is a nonnegative and subadditive positively homogeneous function \(q\) defined on \(M\).
Garcìa-Raffi, L.M. +2 more
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Asymmetric norms given by symmetrisation and specialisation order
Topology and its Applications, 2018A function \(d:X\times X\to [0,\infty)\) of a set \(X\) is called a \(T_0\)-quasi-metric if the following conditions hold for all \(x,y,z\in X\): \[ d(x,x)=0, \] \[ d(x,z)\leq d(x,y)+d(y,z), \] \[ d(x,y)=0=d(y,x) \text{ implies that }x=y. \] The authors in this paper continue the investigation between \(T_0\)-quasi-metric spaces and partially ordered ...
Jurie Conradie, Hans-Peter A. Künzi
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Social norms evolve with asymmetric sanctions
Nature Human Behaviour, 2018How social norms evolve over time and what affects their evolution are central questions in the literature about norms. A study suggests that over time, hygiene and violence norms have become stricter, because those who prefer strict norms sanction those who prefer loose norms more than sanctioning in the other direction.
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Convergence and completeness in asymmetrically normed sequence lattices
Quaestiones Mathematicae, 2015If (X, ∥ · ∥) is a real normed lattice, then p(x) = ∥x+∥ defines anasymmetric norm on X. We give sufficient conditions for (X, p) to be left-K-sequentially complete in the case where X is a normed sequence lattice and investigate the Smyth completeness of the positive cone of such lattices.Keywords: Asymmetrically normed lattice, left-K-sequential ...
Conradie, J.J., Mabula, M.D.
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Convergence and left-K-sequential completeness in asymmetrically normed lattices
Acta Mathematica Hungarica, 2012With \(\mathbb R\), \(\mathbb R^+\), \(\mathbb N\), the sets of real numbers, of positive real numbers and of positive integers, respectively, with \(X\) a real linear space, a function \(p : X\to\mathbb R\) is called an asymmetric norm on \(X\) if, for all \(x,y\in X\) and \(\alpha\in\mathbb R^+\), (a) \(p(x)=p(-x)=0\) iff \(x=0\), (b) \(p(\alpha x ...
Conradie, J. J., Mabula, M. D.
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Weakly convex sets in asymmetric normed spaces
2017 Constructive Nonsmooth Analysis and Related Topics (dedicated to the memory of V.F. Demyanov) (CNSA), 2017In this work we present different results for weakly convex sets is spaces with asymmetric seminorm. We present the theorem for the well-posedness of the closest points problem and the Separation Theorem for weakly and strongly convex sets w.r.t. a quasiball.
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Asymmetric labor market institutions in the EMU: Positive and normative implications [PDF]
, 2007 How do asymmetric labor market institutions affect the volatility of innovation and unemployment differentials in a currency union? What are the implications for monetary policy? To answer these questions, this paper sets up a DSGE currency union model with unemployment, hiring frictions and real wage rigidities.
Mirko Abbritti, Andreas Mueller
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