scholarly journals A Helly theorem for functions with values in metric spaces

2009 ◽  
Vol 44 (1) ◽  
pp. 159-168 ◽  
Author(s):  
Miloslav Duchoň ◽  
Peter Maličký
Keyword(s):  
Metric Space ◽  
Metric Spaces ◽  
Complete Metric Space ◽  
Type Theorem ◽  
Continuous Functions ◽  
Linear Operators ◽  
Space Of Continuous Functions ◽  
Riesz Theorem ◽  
Helly Theorem

Abstract We present a Helly type theorem for sequences of functions with values in metric spaces and apply it to representations of some mappings on the space of continuous functions. A generalization of the Riesz theorem is formulated and proved. More concretely, a representation of certain majored linear operators on the space of continuous functions into a complete metric space.

scholarly journals Duality of Moduli and Quasiconformal Mappings in Metric Spaces

2020 ◽  
Vol 8 (1) ◽  
pp. 166-181
Author(s):  
Rebekah Jones ◽  
Panu Lahti
Keyword(s):  
Metric Space ◽  
Metric Spaces ◽  
Complete Metric Space ◽  
Poincaré Inequality ◽  
Quasiconformal Mappings ◽  
Duality Relation ◽  
Doubling Measure ◽  
Poincare Inequality ◽  
Family Of Curves ◽  
The Family

AbstractWe prove a duality relation for the moduli of the family of curves connecting two sets and the family of surfaces separating the sets, in the setting of a complete metric space equipped with a doubling measure and supporting a Poincaré inequality. Then we apply this to show that quasiconformal mappings can be characterized by the fact that they quasi-preserve the modulus of certain families of surfaces.

scholarly journals Best Proximity Point for Generalized Proximal Weak Contractions in Complete Metric Space

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Erdal Karapınar ◽  
V. Pragadeeswarar ◽  
M. Marudai
Keyword(s):  
Approximate Solution ◽  
Metric Space ◽  
Existence And Uniqueness ◽  
Metric Spaces ◽  
Best Proximity Point ◽  
Complete Metric Space ◽  
Optimal Approximate Solution ◽  
Weak Contraction ◽  
Complete Metric Spaces ◽  
New Class

We introduce a new class of nonself-mappings, generalized proximal weak contraction mappings, and prove the existence and uniqueness of best proximity point for such mappings in the context of complete metric spaces. Moreover, we state an algorithm to determine such an optimal approximate solution designed as a best proximity point. We establish also an example to illustrate our main results. Our result provides an extension of the related results in the literature.

scholarly journals Suzuki ψF-contractions and some fixed point results

2018 ◽  
Vol 34 (1) ◽  
pp. 93-102
Author(s):  
NICOLAE-ADRIAN SECELEAN ◽  
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Metric Space ◽  
Metric Spaces ◽  
Complete Metric Space ◽  
Continuity Point ◽  
Picard Operator ◽  
Nonlinear Anal ◽  
New Type

The purpose of this paper is to combine and extend some recent fixed point results of Suzuki, T., [A new type of fixed point theorem in metric spaces, Nonlinear Anal., 71 (2009), 5313–5317] and Secelean, N. A. & Wardowski, D., [ψF-contractions: not necessarily nonexpansive Picard operators, Results Math., 70 (2016), 415–431]. The continuity and the completeness conditions are replaced by orbitally continuity and orbitally completeness respectively. It is given an illustrative example of a Picard operator on a non complete metric space which is neither nonexpansive nor expansive and has a unique continuity point.

On a theorem of Brian Fisher in the framework of w-distance

2017 ◽  
Vol 33 (2) ◽  
pp. 199-205
Author(s):  
DARKO KOCEV ◽  
◽  
VLADIMIR RAKOCEVIC ◽  
Keyword(s):  
Fixed Point ◽  
Metric Space ◽  
Metric Spaces ◽  
Fixed Point Theory ◽  
Complete Metric Space ◽  
Point Theory ◽  
Common Fixed Points ◽  
Complete Metric Spaces ◽  
Condition C ◽  
Relaxing Condition

In 1980. Fisher in [Fisher, B., Results on common fixed points on complete metric spaces, Glasgow Math. J., 21 (1980), 165–167] proved very interesting fixed point result for the pair of maps. In 1996. Kada, Suzuki and Takahashi introduced and studied the concept of w–distance in fixed point theory. In this paper, we generalize Fisher’s result for pair of mappings on metric space to complete metric space with w–distance. The obtained results do not require the continuity of maps, but more relaxing condition (C; k). As a corollary we obtain a result of Chatterjea.

scholarly journals Minimal arcs in metric spaces

1975 ◽  
Vol 19 (4) ◽  
pp. 426-430 ◽  
Author(s):  
S. K. Hildebrand ◽  
Harold Willis Milnes
Keyword(s):  
Fixed Points ◽  
Metric Space ◽  
Metric Spaces ◽  
Complete Metric Space ◽  
Minimal Length

In this paper we discuss the existence of an are of minimal length joining two arbitrary, yet fixed points in a complete metric space, where the metric is restricted only by the properties (A) and (B) given below. It is shown that under these conditions an arc of least length joining any two fixed points exists, and is unique. In addition, its length is shown to be equal to the metrie distance between the points.

scholarly journals A Universal Separable Diversity

2017 ◽  
Vol 5 (1) ◽  
pp. 138-151 ◽  
Author(s):  
David Bryant ◽  
André Nies ◽  
Paul Tupper
Keyword(s):  
Metric Space ◽  
Metric Spaces ◽  
Complete Metric Space ◽  
Urysohn Space ◽  
Fundamental Properties ◽  
Finite Set ◽  
Whole Space ◽  
Set Of Points ◽  
Separable Metric Space

AbstractThe Urysohn space is a separable complete metric space with two fundamental properties: (a) universality: every separable metric space can be isometrically embedded in it; (b) ultrahomogeneity: every finite isometry between two finite subspaces can be extended to an auto-isometry of the whole space. The Urysohn space is uniquely determined up to isometry within separable metric spaces by these two properties. We introduce an analogue of the Urysohn space for diversities, a recently developed variant of the concept of a metric space. In a diversity any finite set of points is assigned a non-negative value, extending the notion of a metric which only applies to unordered pairs of points.We construct the unique separable complete diversity that it is ultrahomogeneous and universal with respect to separable diversities.

scholarly journals Compact reduction in Lipschitz-free spaces

2021 ◽  
Vol 151 (6) ◽  
pp. 1683-1699
Author(s):  
Ramón J. Aliaga ◽  
Camille Noûs ◽  
Colin Petitjean ◽  
Antonín Procházka
Keyword(s):  
Banach Space ◽  
Metric Space ◽  
General Principle ◽  
Metric Spaces ◽  
Approximation Property ◽  
Complete Metric Space ◽  
Infinite Dimensional ◽  
Schur Property ◽  
Free Spaces ◽  
Compact Subsets

We prove a general principle satisfied by weakly precompact sets of Lipschitz-free spaces. By this principle, certain infinite dimensional phenomena in Lipschitz-free spaces over general metric spaces may be reduced to the same phenomena in free spaces over their compact subsets. As easy consequences we derive several new and some known results. The main new results are: $\mathcal {F}(X)$ is weakly sequentially complete for every superreflexive Banach space $X$, and $\mathcal {F}(M)$ has the Schur property and the approximation property for every scattered complete metric space $M$.

scholarly journals On some F-contraction of Piri-Kumam-Dung-type mappings in metric spaces

2020 ◽  
Vol 68 (4) ◽  
pp. 697-714 ◽  
Author(s):  
Jelena Vujaković ◽  
Stojan Radenović
Keyword(s):  
Metric Space ◽  
Cauchy Sequence ◽  
Metric Spaces ◽  
Complete Metric Space ◽  
Contraction Mappings ◽  
Picard Sequence ◽  
Increasing Function

Introduction/purpose: This paper establishes some new results of Piri-Kumam-Dung-type mappings in a complete metric space.The goal was to improve the already published results. Methods: Using the property of a strictly increasing function as well as the known Lemma formulated in (Radenović et al, 2017), the authors have proved that a Picard sequence is a Cauchy sequence. Results: New results were obtained concerning the F-contraction mappings of S in a complete metric space. To prove it, the authors used only property (W1). Conclusion:The authors believe that the obtained results represent a significant improvement of many known results in the existing literature.

scholarly journals Compactness Property of Fuzzy Soft Metric Space and Fuzzy Soft Continuous Function

2021 ◽  
pp. 3031-3038
Author(s):  
Raghad I. Sabri
Keyword(s):  
Functional Analysis ◽  
Continuous Function ◽  
Metric Space ◽  
Metric Spaces ◽  
Continuous Functions ◽  
Compactness Property ◽  
Locally Compact ◽  
Fuzzy Metric Spaces ◽  
Fundamental Properties ◽  
Definition Of

      The theories of metric spaces and fuzzy metric spaces are crucial topics in mathematics.    Compactness is one of the most important and fundamental properties that have been widely used in Functional Analysis. In this paper, the definition of compact fuzzy soft metric space is introduced and some of its important theorems are investigated. Also, sequentially compact fuzzy soft metric space and locally compact fuzzy soft metric space are defined and the relationships between them are studied. Moreover, the relationships between each of the previous two concepts and several other known concepts are investigated separately. Besides, the compact fuzzy soft continuous functions are studied and some essential theorems are proved.

scholarly journals Approximation fixed theorems for α-partial weakly Zamfirescu mappings with application to homotopy invariance

Filomat ◽  
2016 ◽  
Vol 30 (7) ◽  
pp. 1941-1956
Author(s):  
Aphinat Ninsri ◽  
Wutiphol Sintunavarat
Keyword(s):  
Fixed Point ◽  
Binary Relation ◽  
Metric Space ◽  
Metric Spaces ◽  
Complete Metric Space ◽  
Homotopy Invariance ◽  
Complete Metric Spaces ◽  
Approximate Fixed Point

In this paper, we introduce the concept of ?-partial weakly Zamfirescu mappings and give some approximate fixed point results for this mapping in ?-complete metric spaces. We also give some approximate fixed point results in ?-complete metric space endowed with an arbitrary binary relation and approximate fixed point results in ?-complete metric space endowed with graph. As application, we give homotopy results for ?-partial weakly Zamfirescu mapping.

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