Uniformly Convex Metric Spaces
Abstract: In this paper the theory of uniformly convex metric spaces is developed. These spaces exhibit ageneralized convexity of the metric from a fixed point. Using a (nearly) uniform convexity property a simpleproof of reflexivity is presented and a weak topology of such spaces is analyzed. This topology, called coconvextopology, agrees with the usually weak topology in Banach spaces. An example of a CAT (0)-spacewith weak topology which is not Hausdorff is given.In the end existence and uniqueness of generalized barycenters is shown, an application to isometric groupactions is given and a Banach-Saks property is proved.
- Location
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Deutsche Nationalbibliothek Frankfurt am Main
- Extent
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Online-Ressource
- Language
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Englisch
- Bibliographic citation
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Uniformly Convex Metric Spaces ; volume:2 ; number:1 ; year:2014 ; extent:22
Analysis and geometry in metric spaces ; 2, Heft 1 (2014) (gesamt 22)
- Creator
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Kell, Martin
- DOI
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10.2478/agms-2014-0015
- URN
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urn:nbn:de:101:1-2024041116451216211562
- Rights
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Open Access; Der Zugriff auf das Objekt ist unbeschränkt möglich.
- Last update
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14.08.2025, 10:57 AM CEST
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Associated
- Kell, Martin
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Fixed point theorems in convex metric spaces
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ON UNIFORMLY CONVEX AND UNIFORMLY 2-CONVEX 2-NORMED SPACES
Mordukhovich Derivatives of the Metric Projection Operator in Uniformly Convex and Uniformly Smooth Banach Spaces
Fixed point theorems for N-generalized hybrid mappings in uniformly convex metric spaces
Common fixed points for some generalized multivalued nonexpansive mappings in uniformly convex metric spaces
Common fixed-point results in uniformly convex Banach spaces
On ??-Firmly Nonexpansive Operators in r-Uniformly Convex Spaces
Iterative methods for monotone nonexpansive mappings in uniformly convex spaces
Fixed point theorems in convex metric spaces
On $$\alpha $$ α -Firmly Nonexpansive Operators in r-Uniformly Convex Spaces
On stability of almost surjective functional equations of uniformly convex Banach spaces
Approximating fixed points of α-nonexpansive mappings in uniformly convex Banach spaces and CAT ( 0 ) spaces
Approximating distance between sets by multivalued coupling with application to uniformly convex Banach spaces
ON UNIFORMLY CONVEX AND UNIFORMLY 2-CONVEX 2-NORMED SPACES
Mordukhovich Derivatives of the Metric Projection Operator in Uniformly Convex and Uniformly Smooth Banach Spaces
Fixed point theorems for N-generalized hybrid mappings in uniformly convex metric spaces
Common fixed points for some generalized multivalued nonexpansive mappings in uniformly convex metric spaces
Common fixed-point results in uniformly convex Banach spaces
On ??-Firmly Nonexpansive Operators in r-Uniformly Convex Spaces
Iterative methods for monotone nonexpansive mappings in uniformly convex spaces
Fixed point theorems in convex metric spaces
On $$\alpha $$ α -Firmly Nonexpansive Operators in r-Uniformly Convex Spaces
On stability of almost surjective functional equations of uniformly convex Banach spaces
Approximating fixed points of α-nonexpansive mappings in uniformly convex Banach spaces and CAT ( 0 ) spaces