KKM Type Theorem and Ky Fan's Inequalities in Abstract Convex Spaces

2011 ◽  
Vol 308-310 ◽  
pp. 121-125
Author(s):  
Gu Sheng Tang
Keyword(s):  
Convex Space ◽  
Type Theorem ◽  
Kkm Mapping ◽  
Abstract Convex Space ◽  
Convex Spaces

In this paper, we first prove some type theorem based on the F-KKM mapping and generalized F-KKM mapping in abstract convex space. From this, we establishsome Ky Fan's inequalities.

scholarly journals Remarks on Weakly KKM Maps in Abstract Convex Spaces

2008 ◽  
Vol 2008 ◽  
pp. 1-10
Author(s):  
Sehie Park
Keyword(s):  
Convex Space ◽  
Kkm Principle ◽  
Abstract Convex Space ◽  
Kkm Maps ◽  
Convex Spaces

A KKM space is an abstract convex space satisfying the KKM principle. We obtain variants of the KKM principle for KKM spaces related to weakly KKM maps and indicate some applications of them. These results properly generalize the corresponding ones inG-convex spaces andϕA-spaces(X,D;{ϕA}A∈〈D〉). Consequently, results by Balaj 2004, Liu 1991, and Tang et al. 2007 can be properly generalized and unified.

scholarly journals Improving KKM Theory on General Metric Type Spaces

2021 ◽  
Vol 9 (1) ◽  
pp. 1-12
Author(s):  
Sehie Park
Keyword(s):  
Convex Space ◽  
Metric Spaces ◽  
Space Theory ◽  
Type Space ◽  
Generalized Metric ◽  
Abstract Convex Space ◽  
Type Spaces

Abstract A generalized metric type space is a generic name for various spaces similar to hyperconvex metric spaces or extensions of them. The purpose of this article is to introduce some KKM theoretic works on generalized metric type spaces and to show that they can be improved according to our abstract convex space theory. Most of these works are chosen on the basis that they can be improved by following our theory. Actually, we introduce abstracts of each work or some contents, and add some comments showing how to improve them.

scholarly journals The H∞-optimization in locally convex spaces

2002 ◽  
Vol 15 (2) ◽  
pp. 91-103
Author(s):  
Chuan-Gan Hu ◽  
Li-Xin Ma
Keyword(s):  
Control Theory ◽  
Convex Space ◽  
Locally Convex Space ◽  
Locally Convex Spaces ◽  
Model Matching ◽  
Matching Error ◽  
Locally Convex ◽  
Convex Spaces

In this paper, the ordinary H∞-control theory is extended to locally convex spaces through the form of a parameter. The algorithms of computing the infimal model-matching error and the infimal controller are presented in a locally convex space. Two examples with the form of a parameter are enumerated for computing the infimal model-matching error and the infimal controller.

scholarly journals Some remarks on countably barrelled and countably quasibarrelled spaces

1967 ◽  
Vol 15 (4) ◽  
pp. 295-296 ◽  
Author(s):  
Sunday O. Iyahen
Keyword(s):  
Convex Space ◽  
Locally Convex Space ◽  
Locally Convex Spaces ◽  
Countable Union ◽  
Bounded Subset ◽  
Linear Subspaces ◽  
Barrelled Spaces ◽  
Locally Convex ◽  
Barrelled Space ◽  
Convex Spaces

Barrelled and quasibarrelled spaces form important classes of locally convex spaces. In (2), Husain considered a number of less restrictive notions, including infinitely barrelled spaces (these are the same as barrelled spaces), countably barrelled spaces and countably quasibarrelled spaces. A separated locally convex space E with dual E' is called countably barrelled (countably quasibarrelled) if every weakly bounded (strongly bounded) subset of E' which is the countable union of equicontinuous subsets of E' is itself equicontinuous. It is trivially true that every barrelled (quasibarrelled) space is countably barrelled (countably quasibarrelled) and a countably barrelled space is countably quasibarrelled. In this note we give examples which show that (i) a countably barrelled space need not be barrelled (or even quasibarrelled) and (ii) a countably quasibarrelled space need not be countably barrelled. A third example (iii)shows that the property of being countably barrelled (countably quasibarrelled) does not pass to closed linear subspaces.

scholarly journals Relatively Cyclic and Noncyclic P-Contractions in Locally ?-Convex Space

Axioms ◽  
2019 ◽  
Vol 8 (3) ◽  
pp. 96
Author(s):  
Edraoui Mohamed ◽  
Aamri Mohamed ◽  
Lazaiz Samih
Keyword(s):  
Fixed Points ◽  
Convex Space ◽  
Existence And Uniqueness ◽  
Locally Convex Space ◽  
Best Proximity Points ◽  
Locally Convex ◽  
Convex Spaces

Our main goal of this research is to present the theory of points for relatively cyclic and relatively relatively noncyclic p-contractions in complete locally K -convex spaces by providing basic conditions to ensure the existence and uniqueness of fixed points and best proximity points of the relatively cyclic and relatively noncyclic p-contractions map in locally K -convex spaces. The result of this paper is the extension and generalization of the main results of Kirk and A. Abkar.

On nearly uniformly convex and k-uniformly convex spaces

1984 ◽  
Vol 95 (2) ◽  
pp. 325-327 ◽  
Author(s):  
V. I. Istrăt‚escu ◽  
J. R. Partington
Keyword(s):  
Banach Space ◽  
Convex Space ◽  
Normal Structure ◽  
Uniformly Convex ◽  
Uniformly Convex Space ◽  
Uniformly Convex Spaces ◽  
Convex Spaces

AbstractIn this note we prove that every nearly uniformly convex space has normal structure and that K-uniformly convex spaces are super-reflexive.We recall [1] that a Banach space is said to be Kadec–Klee if whenever xn → x weakly and ∥n∥ = ∥x∥ = 1 for all n then ∥xn −x∥ → 0. The stronger notions of nearly uniformly convex spaces and uniformly Kadec–Klee spaces were introduced by R. Huff in [1]. For the reader's convenience we recall them here.

scholarly journals (L,M)-fuzzy topological-convex spaces

Filomat ◽  
2019 ◽  
Vol 33 (19) ◽  
pp. 6435-6451 ◽  
Author(s):  
Xiu-Yun Wu ◽  
Chun-Yan Liao
Keyword(s):  
Convex Space ◽  
One To One ◽  
Convex Spaces

In this paper, the notion of (L,M)-fuzzy topological-convex spaces is introduced and some of its characterizations are obtained. Then the notion of (L,M)-fuzzy convex enclosed relation spaces is introduced and its one-to-one correspondence with (L,M)-fuzzy convex space is studied. Based on this, the notion of (L,M)-fuzzy topological-convex enclosed relation spaces is introduced and its categorical isomorphism to (L,M)-fuzzy topological-convex spaces is discussed.

scholarly journals Global Schauder decompositions of locally convex spaces

2007 ◽  
Vol 101 (1) ◽  
pp. 65
Author(s):  
Milena Venkova
Keyword(s):  
Convex Space ◽  
Entire Functions ◽  
Locally Convex Space ◽  
Locally Convex Spaces ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Necessary And Sufficient ◽  
Locally Convex ◽  
Convex Spaces

We define global Schauder decompositions of locally convex spaces and prove a necessary and sufficient condition for two spaces with global Schauder decompositions to be isomorphic. These results are applied to spaces of entire functions on a locally convex space.

Subspaces with property (b) in locally convex spaces of quasi-barrelled type

1980 ◽  
Vol 88 (2) ◽  
pp. 331-337 ◽  
Author(s):  
Bella Tsirulnikov
Keyword(s):  
Convex Space ◽  
Locally Convex Space ◽  
Dense Subspace ◽  
Locally Convex Spaces ◽  
Linear Hull ◽  
Bounded Set ◽  
Property B ◽  
Locally Convex ◽  
Strong Dual ◽  
Convex Spaces

A subspace G of a locally convex space E has property (b) if for every bounded set B of E the codimension of G in the linear hull of G ∪ B is finite, (5). Extending the results of (5) and (14), we prove that, if the strong dual of E is complete, then subspaces with property (b) inherit the following properties of E: σ-evaluability, evaluability, the property of being Mazur, semibornological and bornological. We also prove that a dense subspace with property (b) of a Mazur space is sequentially dense, and of a semibornological space – dense in the sense of Mackey (locally dense, following M. Valdivia).

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