Results 261 to 270 of about 370,928 (312)

Convexities of metric spaces

Geometriae Dedicata, 2007
The most common and therefore also most extensively studied non-positive curvature conditions for metric spaces are the ones due to Alexandrov on the one hand and due to Busemann on the other hand. Whereas the latter one describes the convexity of the distance function in a certain sense, the \(\text{CAT}(0)\)-condition can be viewed as a uniform ...
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Convex feasibility problems on uniformly convex metric spaces

Optimization Methods and Software, 2018
In this paper, we extend two important notions, weighted average method and Mann's iterative method, in the study of convex feasibility problem for general maps defined on p-uniformly convex metric...
Byoung Jin Choi, Un Cig Ji, Yongdo Lim
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Convexity in finite metric spaces

Geometriae Dedicata, 1994
A subset \(S\) of a metric space \((X,d)\) is called \(d\)-convex if for every pair of points \(x, y \in S\) all the points between \(x\) and \(y\) belong to \(S\). Let \({\mathfrak C}_ d\) be the family of all \(d\)-convex subsets of \((X,d)\). Then \((X, {\mathfrak C}_ d)\) is a convexity structure (Prop.
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Convex linear metric spaces are normable

The Journal of Analysis, 2019
The authors call a linear metric space \((X,d)\) over the field \(\mathbb R\) convex if \(d(\lambda x+(1-\lambda)y,0)\le\lambda d(x,0)+(1-\lambda)d(y,0)\) holds for all \(x,y\in X\) and each \(\lambda\), \(0\le\lambda\le1\). They prove that each (real) convex linear metric space is normable (with the norm given by \(\|x\|=d(x,0)\).
Jitender Singh, T. D. Narang
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Φ-Convex Functions Defined on Metric Spaces

Journal of Mathematical Sciences, 2003
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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? K -convex functions on metric spaces

manuscripta mathematica, 2003
By an ℱK-convex function on a length metric space, we mean one that satisfies fn ≥ −Kf on all unitspeed geodesics. We show that natural ℱK-convex (-concave) functions occur in abundance on metric spaces of curvature bounded above (below) by K in the sense of Alexandrov.
Stephanie Alexander, Richard L. Bishop
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Maximal convex metrics on some classical metric spaces

Geometriae Dedicata, 1989
A metric d is said to have maximal symmetry iff its isometry group is not properly contained in the isometry group of any metric equivalent to d. Theorem. Every convex, two-point homogeneous metric for which small spheres are connected has maximal symmetry. Corollary.
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Fixed point theorems for set-valued G-contractions in a graphical convex metric space with applications

Journal of Fixed Point Theory and Applications, 2020
Lili Chen, N. Yang, Yanfeng Zhao, Zhenhua Ma   +3 more
semanticscholar   +1 more source

Metric Entropy of Convex Hulls in Banach Spaces

Journal of the London Mathematical Society, 1999
The \(n\)th entropy number \(\varepsilon_n(A)\) of a bounded set \(A\) is the infimum of those \(\varepsilon\) for which \(A\) can be covered by \(n\) balls of radius \(\varepsilon\). If \(A\) is relatively compact, this sequence obviously converges to zero. The authors' main purpose is to show that if the sequence of entropy numbers (is dominated by a
Carl, Bernd, Kyrezi, Ioanna, Pajor, Alain   +2 more
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On Strictly Convex Linear Metric Spaces

Creative Mathematics and Informatics
Ahuja, Narangand Trehan extended the concept of strict convexity from normed linear spaces to linear metric spaces [G. C. Ahuja, T. D Narang, andS. Trehan. Best approximation on convexsets in metric linear spaces. Math. Nachr. 78 (1977), no.1, 125-130] and since then, various other forms of strict convexity in linear metric spaces have emerged in ...
HARPREET K. GROVER, SHELLY GARG, T.D. NARANG   +2 more
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