scholarly journals Asymptotic farthest points and extreme points

Filomat ◽  
2018 ◽  
Vol 32 (17) ◽  
pp. 5875-5885
Author(s):  
Nejhad Ardakani ◽  
Mazaheri Tehrani
Keyword(s):  
Functional Analysis ◽  
Approximation Theory ◽  
Normed Space ◽  
Extreme Points ◽  
Bounded Sequence ◽  
Bounded Subset ◽  
Farthest Points ◽  
Farthest Point

Let X be a normed space, G a nonempty bounded subset of X and fxng a bounded sequence in X. In this article, we introduce and discuss the concept of asymptotic farthest points of fxng in G, which is a new definition in abstract approximation theory. Then, by applying the topics of functional analysis, we investigate the relation between this new concept and the concepts of extreme points and convexity. In particular, one of the main purposes of this paper is to study conditions under which the existence (uniqueness) of asymptotic farthest point of fxng in G is equivalent to the existence (uniqueness) of asymptotic farthest point of fxng in ext(G) or co(G).

scholarly journals Farthest Points and Subdifferential in -Normed Spaces

2008 ◽  
Vol 2008 ◽  
pp. 1-6
Author(s):  
S. Hejazian ◽  
A. Niknam ◽  
S. Shadkam
Keyword(s):  
Compact Subset ◽  
Normed Space ◽  
Dense Subset ◽  
Normed Spaces ◽  
Point Mapping ◽  
Farthest Points ◽  
Farthest Point ◽  
In Virtue Of

We study the farthest point mapping in a -normed space in virtue of subdifferential of , where is a weakly sequentially compact subset of . We show that the set of all points in which have farthest point in contains a dense subset of .

scholarly journals On Simultaneous Farthest Points in

2011 ◽  
Vol 2011 ◽  
pp. 1-10
Author(s):  
Sh. Al-Sharif ◽  
M. Rawashdeh
Keyword(s):  
Banach Space ◽  
Bounded Subset ◽  
Farthest Points ◽  
Integrable Functions

Let be a Banach space and let be a closed bounded subset of . For , we set  . The set is called simultaneously remotal if, for any , there exists such that  . In this paper, we show that if is separable simultaneously remotal in , then the set of -Bochner integrable functions, , is simultaneously remotal in . Some other results are presented.

scholarly journals On Exposed and Farthest Points in Normed Linear Spaces

1971 ◽  
Vol 12 (3) ◽  
pp. 301-308 ◽  
Author(s):  
M. Edelstein ◽  
J. E. Lewis
Keyword(s):  
Linear Space ◽  
Normed Linear Space ◽  
Nonempty Subset ◽  
Linear Spaces ◽  
Farthest Points ◽  
Normed Linear Spaces ◽  
Farthest Point ◽  
Image Position

Let S be a nonempty subset of a normed linear space E. A point s0 of S is called a farthest point if for some x ∈ E, . The set of all farthest points of S will be denoted far (S). If S is compact, the continuity of distance from a point x of E implies that far (S) is nonempty.

scholarly journals Non-archimedean closed graph theorems

Filomat ◽  
2018 ◽  
Vol 32 (11) ◽  
pp. 3933-3945
Author(s):  
Toivo Leiger
Keyword(s):  
Final Section ◽  
Bounded Sequence ◽  
Bounded Subset ◽  
Closed Graph ◽  
Graph Theorem ◽  
Closed Graph Theorem ◽  
Linear Maps ◽  
Local Convex ◽  
Locally Convex ◽  
Convex Spaces

We consider linear maps T: X ? Y, where X and Y are polar local convex spaces over a complete non-archimedean field K. Recall that X is called polarly barrelled, if each weakly* bounded subset in the dual X0 is equicontinuous. If in this definition weakly* bounded subset is replaced by weakly* bounded sequence or sequence weakly* converging to zero, then X is said to be l?-barrelled or c0-barrelled, respectively. For each of these classes of locally convex spaces (as well as the class of spaces with weakly* sequentially complete dual) as domain class, the maximum class of range spaces for a closed graph theorem to hold is characterized. As consequences of these results, we obtain non-archimedean versions of some classical closed graph theorems. The final section deals with the necessity of the above-named barrelledness-like properties in closed graph theorems. Among others, counterparts of the classical theorems of Mahowald and Kalton are proved.

scholarly journals Properties of Fuzzy Compact Linear Operators on Fuzzy Normed Spaces

2019 ◽  
Vol 16 (1) ◽  
pp. 0104
Author(s):  
Kider Et al.
Keyword(s):  
Compact Operator ◽  
Normed Space ◽  
Bounded Operator ◽  
Convergent Subsequence ◽  
Compact Operators ◽  
Bounded Sequence ◽  
Linear Operators ◽  
Fuzzy Normed Space ◽  
Basic Properties ◽  
Definition Of

In this paper the definition of fuzzy normed space is recalled and its basic properties. Then the definition of fuzzy compact operator from fuzzy normed space into another fuzzy normed space is introduced after that the proof of an operator is fuzzy compact if and only if the image of any fuzzy bounded sequence contains a convergent subsequence is given. At this point the basic properties of the vector space FC(V,U)of all fuzzy compact linear operators are investigated such as when U is complete and the sequence ( ) of fuzzy compact operators converges to an operator T then T must be fuzzy compact. Furthermore we see that when T is a fuzzy compact operator and S is a fuzzy bounded operator then the composition TS and ST are fuzzy compact operators. Finally, if T belongs to FC(V,U) and dimension of V is finite then T is fuzzy compact is proved.

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