Last edited by Samujar
Monday, July 20, 2020 | History

2 edition of Extension of uniformly continuous transformations and hyperconvex metric spaces found in the catalog.

Extension of uniformly continuous transformations and hyperconvex metric spaces

Nachman Aronszajn

# Extension of uniformly continuous transformations and hyperconvex metric spaces

## by Nachman Aronszajn

Written in English

Subjects:
• Functional analysis.

• Edition Notes

Includes bibliography.

The Physical Object ID Numbers Statement by N. Aronszajn and P. Panitchpakdi. Series National Science Foundation. Research project on geometry of function space. Report -- no. 1., Report (National Science Foundation (U.S.). Research Project on Geometry of Function Space)) -- no. 1. Contributions Panitchpakdi, P. Pagination 65 p. Number of Pages 65 Open Library OL16592237M

of a hyperconvex metric space is due to Aronszajn and Pantichpakdi 6. Deﬁnition A metric space M,d is said to be a hyperconvex metric space if for any collection of points x α of M and any collection r α of nonnegative real numbers with d x α,x β ≤r α. A query regarding the uniformly continuous nature of continuous functions from compact metric spaces to metric spaces. 0 Compact Space: Locally Continuous \$\implies\$ Uniformly Continuous.

Aronszajn N, Panitchpakdi P. Extensions of uniformly continuous transformations and hyperconvex metric spaces[J]. Pacific J Math,,– Google Scholar [5] Bardaro C, Ceppitelli R. Some further generalization of the Knaster-Kuratowski-Mazurkiewicz theorem and minimax inequalities[J]. Objects. The empty metric space is the initial object of Met; any singleton metric space is a terminal e the initial object and the terminal objects differ, there are no zero objects in Met.. The injective objects in Met are called injective metric ive metric spaces were introduced and studied first by Aronszajn & Panitchpakdi (), prior to the study of Met as a.

Since one of the most interesting concepts in the theory of hyperconvex metric spaces is the Extension of uniformly continuous transformations and hyperconvex metric spaces, Paciﬁc J. Math. 6(), – [4] Bayod. Metric Spaces Introduction 3 The real numbers R 3 Continuous mappings in E 5 The triangle inequality in E 7 The triangle inequality in R™ 8 Brouwer's Fixed Point Theorem 10 Exercises 11 Metric Spaces 13 The metric topology 15 Examples of metric spaces 19 Completeness 26 Separability and connectedness

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### Extension of uniformly continuous transformations and hyperconvex metric spaces by Nachman Aronszajn Download PDF EPUB FB2

A metric space is injective if and only if it is an injective object in the category of metric spaces and metric maps. For additional properties of injective spaces see Espínola & Khamsi (). References. Aronszajn, N.; Panitchpakdi, P.

"Extensions of uniformly continuous transformations and hyperconvex metric spaces". N. Aronszajn, P. Panitchpakdi, Extension of uniformly continuous transformations and hyperconvex metric spaces.

Pacific J. Math. 6, Author: William Kirk, Naseer Shahzad. The proof presented here seems to be of independent interest, since it is more direct, e.g., it does not rely on the Axiom of choice. References [ 1 ] N. Aronszajn and P. Panitchpakdi, Extension of uniformly continuous transformations and hyperconvex metric spaces, Pacific J.

Math. 6 () [2]Cited by: Continuous Extension of Densely Defined Continuous (but not Uniformly Continuous) Function. 0 Every continuous function on Q can be extended to R continuously. ls it true or false. Continuous Selections of Lipschitz Extensions in Metric Spaces.

When the target space is hyperconvex one can obtain in fact nonexpansivity. It is an open question whether such spaces with. these metric spaces offer a nice example of uniformly convex metric spaces. It is not clear that the main inequality used in Extension of uniformly continuous transformations and hyperconvex.

N. Aronszajn, P. PanitchpakdiExtensions of uniformly continuous transformations and hyperconvex metric spaces Pacific J. Math., 6 (), pp. Google Scholar. N. Aronszajn, P.

PanitchpakdiExtension of uniformly continuous transformations and hyperconvex metric spaces Pacific J. Math., 6 (), pp. Google Scholar. Correction to: ``Extension of uniformly continuous transformations in hyperconvex metric spaces''. Pacific Journal of Mathematics volume 7, issue 4, (), pp.

Project Euclid:   N Aronszajn, P PanitchpakdiExtension of uniformly continuous transformations and hyperconvex metric spaces Pacific J. Math., 6 (), pp. Google Scholar. Let M be a bounded hyperconvex metric space. Let T: M → M be a strongly asymptotic pointwise contraction.

Then T has a unique fixed point, x 0. Moreover the orbit {T n (x)} converges to x 0, for each x ∈ M. Next we relax the strong behavior of T but assume that types are convex to obtain the following result.

Theorem Let M be a bounded. Aronszajn and P. Panitchpakdi, Extensions of uniformly continuous transformations and hyperconvex metric spaces, Pacific J.

Math. 6 () – Crossref, Google Scholar 6. [1] N. Aronszajn, P. Panitchpakdi, Extensions of uniformly continuous transformations and hyperconvex metric spaces, Pacific J. Math. 6 (), Cited on 66 and [2] M. Bridson, A. Haefliger, Metric Spaces of Non-Positive Curvature, Grundlehren der Mathematischen WissenschaftenSpringer-Verlag, Berlin, Cited on N.

Aronszajn, and P. Panitchpakdi, Extension of uniformly continuous transformations and hyperconvex metric spaces, Pacific J. Math. 6 (), – MathSciNet zbMATH Google Scholar. Aronszajn and P. Panitchpakdi, Extension of uniformly continuous transformations and hyperconvex metric spaces, Pacific J.

Math. 6 (), MR c [ADL] J. Ayerbe Toledano, T. Dominguez Benavides, and G. Lopez Acedo, Measures of Noncompactness in Metric Fixed Point Theory, Operator Theory: Advances and Applications In this paper, it was clearly noted that most works including [22] on the KKM theory for hyperconvex metric spaces are simple consequences of much more general results on C-spaces due to Horvath.

Aronszain] Aronszajn, P. Panitchpakdi, "Extensions of uniformly continuous transformations and hyperconvex metric spaces" Pacific J. Math., 6 () pp. – MR [a2] M. Atsuji, "Uniform continuity of continuous functions of metric spaces" Pacific J. Math., 8 () pp. 11–16 MR Zbl Hyperconvex metric spaces, Cartan-Hadamard manifolds and more generally Hadamard spaces or metric spaces with non positive curvature in the sense of Busemann are continuous midpoint spaces.

Theorem A. [14, Theorem ] In the sequel we show that by restricting consideration to mappings with values in hyperconvex metric spaces (which are a special case of an l.c.-space [6]), that. In this article, we introduce a new approach to common fixed point theory for a weak compatible pair.

We first introduce the concepts of R-pair and NR-pair and establish some new common fixed point theorems for a weak compatible pair in hyperconvex metric spaces and uniformly convex metric spaces.

We shall also establish the well-known De Marr's theorem for a family of weak compatible pairs in. Hyperconvex metric spaces were introduced by Aronszajn and Panitchpakdi in in relation to the problem of extending uniformly continuous mappings defined between metric spaces.

It was obvious from the very beginning that the structure given by the hyperconvexity of the metric to the space was a very rich one.It is shown that a set-valued mapping of a hyperconvex metric space which takes values in the space of nonempty externally hyperconvex subsets of always has a lipschitzian single valued selection which satisfies for all.

Extensions of uniformly continuous transformations and hyperconvex metric spaces, Pacific J. Math. 6(), Aronszajn N, Panitchpakdi P: Extension of uniformly continuous transformations and hyperconvex metric spaces. Pacific Journal of Mathematics6: – MathSciNet.