Wijsman convergence: A survey

1994 ◽  
Vol 2 (1-2) ◽  
pp. 77-94 ◽  
Author(s):  
Gerald Beer
Keyword(s):  
Wijsman Convergence

scholarly journals The relation between rough Wijsman convergence and asymptotic cones

2016 ◽  
Vol 40 ◽  
pp. 1349-1355 ◽  
Author(s):  
Öznur ÖLMEZ ◽  
Salih AYTAR
Keyword(s):  
Wijsman Convergence ◽  
Asymptotic Cones

Wijsman convergence of convex sets under renorming

1994 ◽  
Vol 22 (2) ◽  
pp. 207-216 ◽  
Author(s):  
Gerald Beer
Keyword(s):  
Convex Sets ◽  
Wijsman Convergence

scholarly journals Bombay hypertopologies

2003 ◽  
Vol 4 (2) ◽  
pp. 421 ◽  
Author(s):  
Giuseppe Di Maio ◽  
Enrico Meccariello ◽  
Somashekhar Naimpally
Keyword(s):  
Topological Space ◽  
Metric Space ◽  
Wijsman Convergence ◽  
Locally Finite ◽  
Simple Result ◽  
Special Cases ◽  
Wijsman Topology

<p>Recently it was shown that, in a metric space, the upper Wijsman convergence can be topologized with the introduction of a new far-miss topology. The resulting Wijsman topology is a mixture of the ball topology and the proximal ball topology. It leads easily to the generalized or g-Wijsman topology on the hyperspace of any topological space with a compatible LO-proximity and a cobase (i.e. a family of closed subsets which is closed under finite unions and which contains all singletons). Further generalization involving a topological space with two compatible LO-proximities and a cobase results in a new hypertopology which we call the Bombay topology. The generalized locally finite Bombay topology includes the known hypertopologies as special cases and moreover it gives birth to many new hypertopologies. We show how it facilitates comparison of any two hypertopologies by proving one simple result of which most of the existing results are easy consequences.</p>

scholarly journals ON λ-ASYMPTOTICALLY WIJSMAN GENERALIZED STATISTICAL CONVERGENCE OF SEQUENCES OF SETS

2013 ◽  
Vol 56 (1) ◽  
pp. 67-77 ◽  
Author(s):  
Bipan Hazarika ◽  
Ayhan Esi
Keyword(s):  
Statistical Convergence ◽  
Asymptotic Equivalence ◽  
Wijsman Convergence ◽  
Convergence Of Sequences ◽  
Definition Of ◽  
Natural Combination

ABSTRACT The concept of Wijsman statistical convergence was defined by [Nuray, F.-Rhoades, B. E.: Statistical convergence of sequences of sets, Fasc. Math. 49 (2012), 1-9]. In this paper we present three definitions which are a natural combination of the definition of asymptotic equivalence, statistical convergence, generalized statistical convergence and Wijsman convergence. In addition, we also present asymptotically equivalent sequences of sets in sense of Wijsman and study some properties of this concept.

scholarly journals ROUGH CONTINUOUS CONVERGENCE OF SEQUENCES OF SETS

2021 ◽  
pp. 619
Author(s):  
Öznur Ölmez ◽  
Hüseyin Albayrak ◽  
Salih Aytar
Keyword(s):  
Distance Functions ◽  
Wijsman Convergence ◽  
Continuous Convergence ◽  
Convergence Of Sequences ◽  
New Type

In this paper, we define a new type of convergence of sequences of sets by using the continuous convergence (or α-convergence) of the sequence of distance functions. Then we proved in which case it is equivalent to rough Wijsman convergence by considering the different values of the roughness degrees.

scholarly journals On Asymptotically Lacunary Statistical Equivalent Set Sequences

2013 ◽  
Vol 2013 ◽  
pp. 1-5 ◽  
Author(s):  
Uğur Ulusu ◽  
Fatih Nuray
Keyword(s):  
Statistical Convergence ◽  
Asymptotic Equivalence ◽  
Wijsman Convergence ◽  
Lacunary Statistical Convergence ◽  
Natural Combination

This paper presents three definitions which are natural combination of the definitions of asymptotic equivalence, statistical convergence, lacunary statistical convergence, and Wijsman convergence. In addition, we also present asymptotically equivalent (Wijsman sense) analogs of theorems in Patterson and Savaş (2006).

scholarly journals On asymptotically Wijsman lacunary statistical convergence of set sequences in ideal context

Filomat ◽  
2017 ◽  
Vol 31 (9) ◽  
pp. 2691-2703 ◽  
Author(s):  
Bipan Hazarika ◽  
Ayhan Esi
Keyword(s):  
Statistical Convergence ◽  
Asymptotic Equivalence ◽  
Wijsman Convergence ◽  
Lacunary Statistical Convergence ◽  
Natural Combination

In this paper, we introduce some definitions which are natural combination of the notions of asymptotic equivalence, statistical convergence, lacunary statistical convergence, Wijsman convergence and ideal. In addition, we also define the concept of asymptotically equivalent sequences of sets in the sense ofWijsman convergence and prove some interesting results related to these concepts.

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