scholarly journals On -Asymptotically Statistical Equivalence of Sequences of Sets

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
Ömer Kışı ◽  
Fatıh Nuray
Keyword(s):  
Statistical Convergence ◽  
Asymptotic Equivalence ◽  
Statistical Equivalence ◽  
Asymptotically Equivalence ◽  
Natural Combination

This paper presents the notion of -asymptotically statistical equivalence, which is a natural combination of asymptotic -equivalence, and -statistical equivalence for sequences of sets. We find its relations to -asymptotically statistical convergence, strong -asymptotically equivalence, and strong Cesaro -asymptotically equivalence for sequences of sets.

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 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.

On asymptotically deferred statistical equivalence of sequences

Filomat ◽  
2017 ◽  
Vol 31 (16) ◽  
pp. 5139-5150 ◽  
Author(s):  
Cem Koşar ◽  
Mehmet Küçükaslan ◽  
Mikail Et
Keyword(s):  
Statistical Equivalence ◽  
Asymptotically Equivalence ◽  
Definition Of

In this study, combining the definition of asymptotically equivalence of sequences and deferred density, the concepts of asymptotically deferred statistical equivalence and strong deferred asymptotically equivalence of nonnegative sequences are introduced. Besides, the main properties of asymptotically deferred statistical equivalence and strong deferred asymptotically equivalence, some inclusion and equivalence results are given.

ON ASYMPTOTICALLY LACUNARY σ-STATISTICAL EQUIVALENT SEQUENCES OF FUZZY NUMBERS

2009 ◽  
Vol 05 (03) ◽  
pp. 589-598 ◽  
Author(s):  
EKREM SAVAŞ
Keyword(s):  
Statistical Convergence ◽  
Fuzzy Numbers ◽  
Invariant Mean ◽  
Lacunary Statistical Convergence ◽  
Sequences Of Fuzzy Numbers ◽  
Natural Combination

This paper presents the asymptotically lacunary σ-statistical equivalent which is a natural combination of the definition for asymptotically equivalent, invariant mean and lacunary statistical convergence of fuzzy numbers. In addition, we shall also present asymptotically lacunary σ-statistical equivalent analogs of Savas and Nuray's theorems in Ref. 8.

scholarly journals Asymptotically Lacunary Statistical Equivalent Sequences of Fuzzy Numbers - doi: 10.5269/bspm.v30i2.14007

2011 ◽  
Vol 30 (2) ◽  
pp. 57-62
Author(s):  
Ayhan Esi ◽  
Necdet Çatalbas
Keyword(s):  
Statistical Convergence ◽  
Fuzzy Numbers ◽  
Lacunary Sequence ◽  
Lacunary Statistical Convergence ◽  
Sequences Of Fuzzy Numbers ◽  
Natural Combination

In this article we present the following definition which is natural combination of the definition for asymptotically equivalent and lacunary statistical convergence of fuzzy numbers. Let =(k_{r}) be a lacunary sequence. The two sequnces X  = (X_{k}) and Y=(Y_{k}) of fuzzy numbers are said to be asymptotically lacunary statistical equivalent to multiple L provided that for every >0lim_{r}(1/(h_{r}))|{k∈I_{r}:d(((X_{k})/(Y_{k})),L)≥}|=0. 

ON ASYMPTOTICALLY λ-STATISTICAL EQUIVALENT SEQUENCES OF FUZZY NUMBERS

2007 ◽  
Vol 03 (03) ◽  
pp. 301-306 ◽  
Author(s):  
EKREM SAVAŞ
Keyword(s):  
Statistical Convergence ◽  
Fuzzy Numbers ◽  
Sequences Of Fuzzy Numbers ◽  
Natural Combination

This paper presents the following definition which is a natural combination of the definitions for asymptotically equivalent and λ-statistical convergence of fuzzy numbers. The two sequences [X] and [Y] of fuzzy numbers are said to be asymptotically λ-statistical equivalent of multiple L provided that for every ∊ > 0 [Formula: see text] (denoted by [Formula: see text]) and simply asymptotically λ-statistical equivalent if L = 1. In addition, we shall also present asymptotically equivalent analogs of Savas's theorems in Ref. 7.

scholarly journals Asymptotically Lacunary Statistical Equivalence of Double Sequences of Sets

2016 ◽  
Vol 49 (2) ◽  
Author(s):  
F. Nuray ◽  
R. F. Patterson ◽  
E. Dündar
Keyword(s):  
Double Sequences ◽  
Statistical Equivalence ◽  
Asymptotically Equivalence

AbstractThe concepts of Wijsman asymptotically equivalence, Wijsman asymptotically statistically equivalence, Wijsman asymptotically lacunary equivalence and Wijsman asymptotically lacunary statistical equivalence for sequences of sets were studied by Ulusu and Nuray [24]. In this paper, we get analogous results for double sequences of sets.

scholarly journals Wijsman Orlicz Asymptotically Ideal -Statistical Equivalent Sequences

2013 ◽  
Vol 2013 ◽  
pp. 1-9
Author(s):  
Bipan Hazarika
Keyword(s):  
Asymptotic Equivalence ◽  
Equivalent Sequence ◽  
Definition Of ◽  
Natural Combination ◽  
Positive Integers

An ideal is a family of subsets of positive integers which is closed under taking finite unions and subsets of its elements. In this paper, we introduce a new definition of asymptotically ideal -statistical equivalent sequence in Wijsman sense and present some definitions which are the natural combination of the definition of asymptotic equivalence, statistical equivalent, -statistical equivalent sequences in Wijsman sense. Finally, we introduce the notion of Cesaro Orlicz asymptotically -equivalent sequences in Wijsman sense and establish their relationship with other classes.

Approximation in statistical sense to B -continuous functions by positive linear operators

2010 ◽  
Vol 47 (3) ◽  
pp. 289-298 ◽  
Author(s):  
Fadime Dirik ◽  
Oktay Duman ◽  
Kamil Demirci
Keyword(s):  
Compact Subset ◽  
Real Line ◽  
Statistical Convergence ◽  
Approximation Theorem ◽  
Continuous Functions ◽  
Linear Operators ◽  
Positive Linear Operators ◽  
Statistical Approximation ◽  
Classical Version ◽  
Statistical Sense

In the present work, using the concept of A -statistical convergence for double real sequences, we obtain a statistical approximation theorem for sequences of positive linear operators defined on the space of all real valued B -continuous functions on a compact subset of the real line. Furthermore, we display an application which shows that our new result is stronger than its classical version.

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