Results 1 to 10 of about 86 (68)
$k$-smoothness on polyhedral Banach spaces [PDF]
Colloquium Mathematicum, 2022 11 ...
Arpita Mal, Kallol Paul
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Structure of Pareto Solutions of Generalized Polyhedral-Valued Vector Optimization Problems in Banach Spaces [PDF]
Abstract and Applied Analysis, 2013 In general Banach spaces, we consider a vector optimization problem (SVOP) in which the objective is a set-valued mapping whose graph is the union of finitely many polyhedra or the union of finitely many generalized polyhedra.
Qinghai He, Weili Kong
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On the numerical index of polyhedral Banach spaces [PDF]
Linear Algebra and Its Applications, 2019 The computation of the numerical index of a Banach space is an intriguing problem, even in case of two-dimensional real polyhedral Banach spaces. In this article we present a general method to estimate the numerical index of any finite-dimensional real polyhedral Banach space, by considering the action of only finitely many functionals, on the unit ...
Kallol Paul +2 more
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Best approximation in polyhedral Banach spaces
Journal of Approximation Theory, 2011 The authors study conditions under which the metric projection of a polyhedral Banach space \(X\) onto a closed subspace \(Y\) is Hausdorff lower or upper semicontinuous. The paper is organized as follows. Section 0 is an introduction. Section 1 contains notation concerning Banach spaces, followed by definitions and preliminary facts on polyhedral ...
Libor Vesely +2 more
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Smooth and polyhedral approximation in Banach spaces
Journal of Mathematical Analysis and Applications, 2016 We show that norms on certain Banach spaces $X$ can be approximated uniformly, and with arbitrary precision, on bounded subsets of $X$ by $C^{\infty}$ smooth norms and polyhedral norms. In particular, we show that this holds for any equivalent norm on $c_0(Γ)$, where $Γ$ is an arbitrary set.
Bible, Victor, Smith, Richard J.
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Polyhedral norms on non-separable Banach spaces
Journal of Functional Analysis, 2008 A Banach space \(X\) is called polyhedral if the unit ball of each of its finite-dimensional subspaces is a polytope. Separable polyhedral spaces were investigated in detail; see, e.g., [\textit{V. P. Fonf, J.\,Lindenstrauss} and \textit{R. P. Phelps}, in: Handbook of the Geometry of Banach spaces, Vol.\ I, Elsevier, 599--670 (2001; Zbl 1086.46004 ...
S Troyanski
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A ``hidden'' characterization of approximatively polyhedral convex sets in Banach spaces [PDF]
Studia Mathematica, 2012 For a Banach space $X$ by $Conv_H(X)$ we denote the space of non-empty closed convex subsets of $X$, endowed with the Hausdorff metric. We prove that for any closed convex set $C\subset X$ and its metric component $H_C=\{A\in Conv_H(X):d_H(A,C)0$ there is a polyhedral convex subset $P\subset X$ on Hausdorff distance $d_H(P,C)0$ (resp.
Taras Banakh
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Extension of isometries between unit spheres of finite-dimensional polyhedral Banach spaces
Journal of Mathematical Analysis and Applications, 2012 We prove that an onto isometry between unit spheres of finite-dimensional polyhedral Banach spaces extends to a linear isometry of the corresponding spaces.
Vladimir Kadets, MIGUEL Martin
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Polyhedral direct sums of Banach spaces, and generalized centers of finite sets
Journal of Mathematical Analysis and Applications, 2012 Let \(X\) be a real Banach space. \(X\) is said to satisfy \((GC)\) if for every \(n\) and for every real-valued continuous, nondecreasing coercive function \(f\) on \( [0,\infty)^n\), the set \(E_f(a)\) of minimizers of the function \(\phi(x) = f(\|x-a_1\|,\dots,\|x-a_n\|)\) is nonempty, where \(x \in X\) and \(a= (a_1,\dots,a_n) \in X^n\).
Libor Vesely
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A Note on Polyhedral Banach Spaces [PDF]
Proceedings of the American Mathematical Society, 1972 We give a sufficient condition for an infinitedimensional Banach space X to be polyhedral. If X
Gleit, Alan, McGuigan, Robert
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