Displaying similar documents to “A characterization of sets in with DC distance function”

On operators from to or to

Christian Samuel (2010)

Colloquium Mathematicae

Similarity:

We show that every operator from to is compact when 1 ≤ p,q < s and that every operator from to is compact when 1/p + 1/q > 1 + 1/s.

Generalized versions of Ilmanen lemma: Insertion of or functions

Václav Kryštof (2018)

Commentationes Mathematicae Universitatis Carolinae

Similarity:

We prove that for a normed linear space , if is continuous and semiconvex with modulus , is continuous and semiconcave with modulus and , then there exists such that . Using this result we prove a generalization of Ilmanen lemma (which deals with the case ) to the case of an arbitrary nontrivial modulus . This generalization (where a function is inserted) gives a positive answer to a problem formulated by A. Fathi and M. Zavidovique in 2010.

-points vs -points and -points

Jorge Martinez, Warren Wm. McGovern (2022)

Commentationes Mathematicae Universitatis Carolinae

Similarity:

In a Tychonoff space , the point is called a -point if every real-valued continuous function on can be extended continuously to . Every point in an extremally disconnected space is a -point. A classic example is the space consisting of the countable ordinals together with . The point is known to be a -point as well as a -point. We supply a characterization of -points in totally ordered spaces. The remainder of our time is aimed at studying when a point in a product space...

A localization property for and spaces

Hans Triebel (1994)

Studia Mathematica

Similarity:

Let , where the sum is taken over the lattice of all points k in having integer-valued components, j∈ℕ and . Let be either or (s ∈ ℝ, 0 < p < ∞, 0 < q ≤ ∞) on The aim of the paper is to clarify under what conditions is equivalent to .

On compactness and connectedness of the paratingent

Wojciech Zygmunt (2016)

Annales Universitatis Mariae Curie-Sklodowska, sectio A – Mathematica

Similarity:

In this note we shall prove that for a continuous function , where ,  the paratingent of at is a non-empty and compact set in if and only if satisfies Lipschitz condition in a neighbourhood of . Moreover, in this case the paratingent is a connected set.

On almost everywhere differentiability of the metric projection on closed sets in ,

Tord Sjödin (2018)

Czechoslovak Mathematical Journal

Similarity:

Let be a closed subset of and let denote the metric projection (closest point mapping) of onto in -norm. A classical result of Asplund states that is (Fréchet) differentiable almost everywhere (a.e.) in in the Euclidean case . We consider the case and prove that the th component of is differentiable a.e. if and satisfies Hölder condition of order if .

-regularity for the -equation with a support condition

Shaban Khidr, Osama Abdelkader (2017)

Czechoslovak Mathematical Journal

Similarity:

Let be a -convex intersection, , , in a complex manifold of complex dimension , , and let be a holomorphic vector bundle of rank over . In this paper, -estimates, , for solutions to the -equation with small loss of smoothness are obtained for -valued -forms on when . In addition, we solve the -equation with a support condition in -spaces. More precisely, we prove that for a -closed form in , , , with compact support and for with there...

Theoretical analysis for - minimization with partial support information

Haifeng Li, Leiyan Guo (2025)

Applications of Mathematics

Similarity:

We investigate the recovery of -sparse signals using the - minimization model with prior support set information. The prior support set information, which is believed to contain the indices of nonzero signal elements, significantly enhances the performance of compressive recovery by improving accuracy, efficiency, reducing complexity, expanding applicability, and enhancing robustness. We assume -sparse signals with the prior support which is composed of true indices and wrong...

-products revisited

Reynaldo Rojas-Hernández (2015)

Commentationes Mathematicae Universitatis Carolinae

Similarity:

We show that any -product of at most -many -spaces has the -property. This result generalizes some known results about -spaces. On the other hand, we prove that every -product of monotonically monolithic spaces is monotonically monolithic, and in a similar form, we show that every -product of Collins-Roscoe spaces has the Collins-Roscoe property. These results generalize some known results about the Collins-Roscoe spaces and answer some questions due to Tkachuk [Lifting the Collins-Roscoe...

On linear preservers of two-sided gut-majorization on

Asma Ilkhanizadeh Manesh, Ahmad Mohammadhasani (2018)

Czechoslovak Mathematical Journal

Similarity:

For it is said that is gut-majorized by , and we write , if there exists an -by- upper triangular g-row stochastic matrix such that . Define the relation as follows. if is gut-majorized by and is gut-majorized by . The (strong) linear preservers of on and strong linear preservers of this relation on have been characterized before. This paper characterizes all (strong) linear preservers and strong linear preservers of on and .

Renormings of and the minimal displacement problem

Łukasz Piasecki (2014)

Annales Universitatis Mariae Curie-Sklodowska, sectio A – Mathematica

Similarity:

The aim of this paper is to show that for every Banach space containing asymptotically isometric copy of the space there is a bounded, closed and convex set with the Chebyshev radius such that for every there exists a -contractive mapping with for any .

More on exposed points and extremal points of convex sets in and Hilbert space

Stoyu T. Barov (2023)

Commentationes Mathematicae Universitatis Carolinae

Similarity:

Let be a separable real Hilbert space, with , and let be convex and closed in . Let be a collection of linear -subspaces of . A point is called exposed by if there is a so that . We show that, under some natural conditions, can be reconstituted as the convex hull of the closure of all its exposed by points whenever is dense and . In addition, we discuss the question when the set of exposed by some points forms a -set.

On the Schröder equation

M. Kuczma

Similarity:

CONTENTSPART IIntroduction............................................................................................... 31. General solution.................................................................................. 42. Preliminaries and notation................................................................ 53. solutions in *................................................ 74. Change of variables..............................................................................

On a question of Schmidt and Summerer concerning -systems

Johannes Schleischitz (2020)

Communications in Mathematics

Similarity:

Following a suggestion of W.M. Schmidt and L. Summerer, we construct a proper -system with the property . In fact, our method generalizes to provide -systems with , for arbitrary . We visualize our constructions with graphics. We further present explicit examples of numbers that induce the -systems in question.

On the -fold symmetric product of a space with a --property -network (-network)

Luong Q. Tuyen, Ong V. Tuyen (2020)

Commentationes Mathematicae Universitatis Carolinae

Similarity:

We study the relation between a space satisfying certain generalized metric properties and its -fold symmetric product satisfying the same properties. We prove that has a --property -network if and only if so does . Moreover, if is regular then has a --property -network if and only if so does . By these results, we obtain that is strict -space (strict -space) if and only if so is .