Fixed Point Theory in Hyperconvex Metric Spaces

Espínola, Rafael; Fernández-León, Aurora

doi:10.1007/978-3-319-01586-6_4

Cited by 5 publications

(6 citation statements)

References 65 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…As a corollary of this theorem and Theorem 3.1, we have the fixed point result for nonexpansive multivalued mappings (for more on this see [21,Section 9] Different interesting papers on extensions of the above result have appeared after the publication of [21]; some of them are [11,14,19,34,46]. Also a number of works have been published about KKM mappings on hyperconvex spaces after [33] as, for instance, [15].…”

Section: Definition 32 Givenmentioning

confidence: 90%

Metric fixed point theory on hyperconvex spaces: recent progress

Espínola

Lorenzo

2012

Arab. J. Math.

View full text Add to dashboard Cite

In this survey we present an exposition of the development during the last decade of metric fixed point theory on hyperconvex metric spaces. Therefore we mainly cover results where the conditions on the mappings are metric. We will recall results about proximinal nonexpansive retractions and their impact into the theory of best approximation and best proximity pairs. A central role in this survey will be also played by some recent developments on R-trees. Finally, some considerations and new results on the extension of compact mappings will be shown. Mathematics Subject Classification

show abstract

Section: Definition 32 Givenmentioning

confidence: 90%

Metric fixed point theory on hyperconvex spaces: recent progress

Espínola

Lorenzo

2012

Arab. J. Math.

View full text Add to dashboard Cite

show abstract

“…Hyperconvex metric spaces exhibit a large number of nice properties as being injective metric spaces and absolute nonexpansive retracts. The interested reader may check recent monographs as [6,7] for these and more properties on hyperconvexity and tight spans.…”

Section: [66]mentioning

confidence: 99%

On the gluing of hyperconvex metrics and diversities

Piątek

2014

Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica

View full text Add to dashboard Cite

show abstract

“…Diversities were first introduced by [3] and it quickly became apparent that the concept leads to a rich and useful new area of mathematical theory and applications. Remarkable analogues have arisen between the non-linear analysis of metric spaces and diversity theory [6,8,12] with a new and more general fixed point theorem for non-expansive maps being established by Espínola and Pia ¸tek [7,8]. Diversity theory has led to new work in topology [13] and model theory [5].…”

Section: Introductionmentioning

confidence: 99%

Constant Distortion Embeddings of Symmetric Diversities

Bryant

Tupper

2016

Analysis and Geometry in Metric Spaces

View full text Add to dashboard Cite

Diversities are like metric spaces, except that every nite subset, instead of just every pair of points, is assigned a value. Just as there is a theory of minimal distortion embeddings of nite metric spaces into L , there is a similar, yet undeveloped, theory for embedding nite diversities into the diversity analogue of L spaces. In the metric case, it is well known that an n-point metric space can be embedded into L with O(log n) distortion. For diversities, the optimal distortion is unknown. Here, we establish the surprising result that symmetric diversities, those in which the diversity (value) assigned to a set depends only on its cardinality, can be embedded in L with constant distortion.

show abstract

Fixed Point Theory in Hyperconvex Metric Spaces

Cited by 5 publications

References 65 publications

Metric fixed point theory on hyperconvex spaces: recent progress

Metric fixed point theory on hyperconvex spaces: recent progress

On the gluing of hyperconvex metrics and diversities

Constant Distortion Embeddings of Symmetric Diversities

Contact Info

Product

Resources

About