On weak drop property and quasi-weak drop property

J. H. Qiu

Displaying similar documents to “On weak drop property and quasi-weak drop property”

Structure of efficient sets for strictly quasi convex objectives.

Malivert, C., Boissard, N. (1994)

Journal of Convex Analysis

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On the quasi-weak drop property

J. H. Qiu (2002)

Studia Mathematica

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A new drop property, the quasi-weak drop property, is introduced. Using streaming sequences introduced by Rolewicz, a characterisation of the quasi-weak drop property is given for closed bounded convex sets in a Fréchet space. From this, it is shown that the quasi-weak drop property is equivalent to weak compactness. Thus a Fréchet space is reflexive if and only if every closed bounded convex set in the space has the quasi-weak drop property.

Weak countable compactness implies quasi-weak drop property

J. H. Qiu (2004)

Studia Mathematica

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Every weakly countably compact closed convex set in a locally convex space has the quasi-weak drop property.

Drop property on locally convex spaces

Ignacio Monterde, Vicente Montesinos (2008)

Studia Mathematica

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A single technique provides short proofs of some results about drop properties on locally convex spaces. It is shown that the quasi drop property is equivalent to a drop property for countably closed sets. As a byproduct, we prove that the drop and quasi drop properties are separably determined.

Quasi-distinguished and boundedly completed locally convex spaces.

Bella Tsirulnikov (1981)

Revista de la Real Academia de Ciencias Exactas Físicas y Naturales

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On the Glicksberg theorem for locally quasi-convex Schwartz groups

Lydia Außenhofer (2008)

Fundamenta Mathematicae

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We prove that every locally quasi-convex Schwartz group satisfies the Glicksberg theorem for weakly compact sets.

On a weak form of weak quasi-continuity.

Baker, C.W. (2002)

International Journal of Mathematics and Mathematical Sciences

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On co-ordinated quasi-convex functions

M. Emin Özdemir, Ahmet Ocak Akdemir, Çetin Yıldız (2012)

Czechoslovak Mathematical Journal

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A function $f : I \to ℝ$ , where $I \subseteq ℝ$ is an interval, is said to be a convex function on $I$ if $f (t x + (1 - t) y) \leq t f (x) + (1 - t) f (y)$ holds for all $x, y \in I$ and $t \in [0, 1]$ . There are several papers in the literature which discuss properties of convexity and contain integral inequalities. Furthermore, new classes of convex functions have been introduced in order to generalize the results and to obtain new estimations. We define some new classes of convex functions that we name quasi-convex, Jensen-convex, Wright-convex, Jensen-quasi-convex and Wright-quasi-convex...

Equivalent quasi-norms and atomic decomposition of weak Triebel-Lizorkin spaces

Wenchang Li, Jingshi Xu (2017)

Czechoslovak Mathematical Journal

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Recently, the weak Triebel-Lizorkin space was introduced by Grafakos and He, which includes the standard Triebel-Lizorkin space as a subset. The latter has a wide applications in aspects of analysis. In this paper, the authors firstly give equivalent quasi-norms of weak Triebel-Lizorkin spaces in terms of Peetre's maximal functions. As an application of those equivalent quasi-norms, an atomic decomposition of weak Triebel-Lizorkin spaces is given.