scholarly journals Inscribing closed non-σ-lower porous sets into Suslin non-σ-lower porous sets

2005 ◽  
Vol 2005 (3) ◽  
pp. 221-227 ◽  
Author(s):  
Luděk Zajíček ◽  
Miroslav Zelený
Keyword(s):  
Banach Spaces ◽  
Hilbert Spaces ◽  
General Result ◽  
Metric Space ◽  
Complete Metric Space ◽  
General Theorem ◽  
Porous Sets

The main aim of this paper is to prove that every non-σ-lower porous Suslin set in a topologically complete metric space contains a closed non-σ-lower porous subset. In fact, we prove a general result of this type on “abstract porosities.” This general theorem is also applied to ball small sets in Hilbert spaces and toσ-cone-supported sets in separable Banach spaces.

scholarly journals Existence Theorems for Solvability of a Functional Equation Arising in Dynamic Programming

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Deepmala
Keyword(s):  
Decision Making ◽  
Functional Equation ◽  
Dynamic Programming ◽  
Banach Spaces ◽  
Metric Space ◽  
Functional Equations ◽  
Existence Theorems ◽  
Complete Metric Space ◽  
Decision Making Processes

The paper deals with the existence, uniqueness, and iterative approximations of solutions for the functional equations arising in dynamic programming of multistage decision making processes in Banach spacesBC(S)andB(S)and complete metric spaceBB(S), respectively. Our main results extend, improve, and generalize the results due to several authors. Some examples are also given to demonstrate the advantage of our results over existing one in the literature.

scholarly journals Generic continuity of minimal set-valued mappings

1997 ◽  
Vol 63 (2) ◽  
pp. 238-262 ◽  
Author(s):  
W. B. Moors ◽  
J. R. Giles
Keyword(s):  
Banach Space ◽  
Banach Spaces ◽  
Metric Space ◽  
Complete Metric Space ◽  
Minimal Set ◽  
Set Valued Mapping ◽  
Set Valued Mappings ◽  
Permanence Properties ◽  
Generic Continuity ◽  
Sufficiency Conditions

AbstractWe study classes of Banach spaces where every set-valued mapping from a complete metric space into subsets of the Banach space which satisfies certain minimal properties, is single-valued and norm upper semi-continuous at the points of a dense Gδ subset of its domain. Characterisations of these classes are developed and permanence properties are established. Sufficiency conditions for membership of these classes are defined in terms of fragmentability and σ-fragmentability of the weak topology. A characterisation of non membership is used to show that l∞ (N) is not a member of our classe of generic continuity spaces.

scholarly journals Existence and uniqueness of solutions for certain functional equations and system of functional equations arising in dynamic programming

2016 ◽  
Vol 24 (1) ◽  
pp. 3-28
Author(s):  
◽  
Ravi P. Agarwal
Keyword(s):  
Decision Making ◽  
Dynamic Programming ◽  
Banach Spaces ◽  
Metric Space ◽  
Existence And Uniqueness ◽  
Functional Equations ◽  
Complete Metric Space ◽  
Uniqueness Of Solutions ◽  
System Of Functional Equations ◽  
Decision Making Processes

Abstract This paper deals with the existence, uniqueness and iterative approximations of solutions for the functional equations and system of functional equations arising in dynamic programming of multistage decision making processes in Banach spaces and complete metric space, respectively. The results presented in this paper unify and generalize many known results in the literature. Some examples which dwell upon the importance of our results are also illustrated.

On Fixed Point Theorems in Complete Metric Space

2019 ◽  
Vol 10 (7) ◽  
pp. 1419-1425
Author(s):  
Jayashree Patil ◽  
Basel Hardan
Keyword(s):  
Fixed Point ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
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 Sets of periods for chaotic linear operators

2021 ◽  
Vol 115 (2) ◽  
Author(s):  
J. A. Conejero ◽  
F. Martínez-Giménez ◽  
A. Peris ◽  
F. Rodenas
Keyword(s):  
Banach Spaces ◽  
Hilbert Spaces ◽  
Complete Characterization ◽  
Linear Operators

AbstractWe provide a complete characterization of the possible sets of periods for Devaney chaotic linear operators on Hilbert spaces. As a consequence, we also derive this characterization for linearizable maps on Banach spaces.

Topological Completeness of Function Spaces Arising in the Hausdorff Approximation of Functions

1992 ◽  
Vol 35 (4) ◽  
pp. 439-448 ◽  
Author(s):  
Gerald Beer
Keyword(s):  
Approximation Theory ◽  
Metric Space ◽  
Polish Space ◽  
Complete Metric Space ◽  
Approximation Of Functions ◽  
Lower Envelopes ◽  
Constructive Approximation ◽  
Hausdorff Approximation ◽  
Set Of Points ◽  
Completely Metrizable

AbstractLet X be a complete metric space. Viewing continuous real functions on X as closed subsets of X × R, equipped with Hausdorff distance, we show that C(X, R) is completely metrizable provided X is complete and sigma compact. Following the Bulgarian school of constructive approximation theory, a bounded discontinuous function may be identified with its completed graph, the set of points between the upper and lower envelopes of the function. We show that the space of completed graphs, too, is completely metrizable, provided X is locally connected as well as sigma compact and complete. In the process, when X is a Polish space, we provide a simple answer to the following foundational question: which subsets of X × R arise as completed graphs?

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 A characterisation of Hilbert spaces via orthogonality and proximinality

2005 ◽  
Vol 71 (1) ◽  
pp. 107-111
Author(s):  
Fathi B. Saidi
Keyword(s):  
Banach Space ◽  
Hilbert Space ◽  
Banach Spaces ◽  
Hilbert Spaces ◽  
Real Banach Space ◽  
Nonzero Element ◽  
Dimensional Subspace ◽  
Two Dimensional ◽  
Orthogonal Direction ◽  
Open Problems

In this paper we adopt the notion of orthogonality in Banach spaces introduced by the author in [6]. There, the author showed that in any two-dimensional subspace F of E, every nonzero element admits at most one orthogonal direction. The problem of existence of such orthogonal direction was not addressed before. Our main purpose in this paper is the investigation of this problem in the case where E is a real Banach space. As a result we obtain a characterisation of Hilbert spaces stating that, if in every two-dimensional subspace F of E every nonzero element admits an orthogonal direction, then E is isometric to a Hilbert space. We conclude by presenting some open problems.

Sign in / Sign up

Export Citation Format

Share Document