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.

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 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.

scholarly journals Statistical Convergence in Function Spaces

2011 ◽  
Vol 2011 ◽  
pp. 1-11 ◽  
Author(s):  
Agata Caserta ◽  
Giuseppe Di Maio ◽  
Ljubiša D. R. Kočinac
Keyword(s):  
Uniform Convergence ◽  
Statistical Convergence ◽  
Statistical Approach ◽  
Metric Spaces ◽  
Function Spaces ◽  
Strong Uniform Convergence ◽  
Convergence Of Sequences

We study statistical versions of several classical kinds of convergence of sequences of functions between metric spaces (Dini, Arzelà, and Alexandroff) in different function spaces. Also, we discuss a statistical approach to recently introduced notions of strong uniform convergence and exhaustiveness.

scholarly journals Statistical Convergence and Ideal Convergence of Sequences of Functions in 2-Normed Spaces

2011 ◽  
Vol 2011 ◽  
pp. 1-10 ◽  
Author(s):  
Saeed Sarabadan ◽  
Sorayya Talebi
Keyword(s):  
Statistical Convergence ◽  
Normed Spaces ◽  
Ideal Convergence ◽  
Convergence Of Sequences

We present various kinds of statistical convergence andℐ-convergence for sequences of functions with values in 2-normed spaces and obtain a criterion forℐ-convergence of sequences of functions in 2-normed spaces. We also define the notion ofℐ-equistatistically convergence and studyℐ-equi-statistically convergence of sequences of functions.

scholarly journals λ-Statistical Convergence of Sequences of Functions in Intuitionistic Fuzzy Normed Spaces

2012 ◽  
Vol 2012 ◽  
pp. 1-14 ◽  
Author(s):  
Vatan Karakaya ◽  
Necip Şimşek ◽  
Müzeyyen Ertürk ◽  
Faik Gürsoy
Keyword(s):  
Uniform Convergence ◽  
Pointwise Convergence ◽  
Statistical Convergence ◽  
Normed Spaces ◽  
Basic Properties ◽  
Intuitionistic Fuzzy ◽  
Convergence Of Sequences ◽  
Intuitionistic Fuzzy Normed Spaces ◽  
Convergent Sequences

We studyλ-statistically convergent sequences of functions in intuitionistic fuzzy normed spaces. We define concept ofλ-statistical pointwise convergence andλ-statistical uniform convergence in intuitionistic fuzzy normed spaces and we give some basic properties of these concepts.

scholarly journals Lacunary Statistical Convergence in Measure for Double Sequences of Fuzzy Valued Functions

2021 ◽  
Vol 2021 ◽  
pp. 1-12
Author(s):  
Ömer Kişi
Keyword(s):  
Statistical Convergence ◽  
Double Sequence ◽  
Finite Measure ◽  
Measurable Space ◽  
Double Sequences ◽  
Convergence In Measure ◽  
Measurable Functions ◽  
Lacunary Statistical Convergence ◽  
Convergence Of Sequences ◽  
Sequences Of Fuzzy Numbers

Based on the concept of lacunary statistical convergence of sequences of fuzzy numbers, the lacunary statistical convergence, uniformly lacunary statistical convergence, and equi-lacunary statistical convergence of double sequences of fuzzy-valued functions are defined and investigated in this paper. The relationship among lacunary statistical convergence, uniformly lacunary statistical convergence, equi-lacunary statistical convergence of double sequences of fuzzy-valued functions, and their representations of sequences of α -level cuts are discussed. In addition, we obtain the lacunary statistical form of Egorov’s theorem for double sequences of fuzzy-valued measurable functions in a finite measurable space. Finally, the lacunary statistical convergence in measure for double sequences of fuzzy-valued measurable functions is examined, and it is proved that the inner and outer lacunary statistical convergence in measure are equivalent in a finite measure set for a double sequence of fuzzy-valued measurable functions.

scholarly journals On Kuratowski I-convergence of sequences of closed sets

Filomat ◽  
2017 ◽  
Vol 31 (4) ◽  
pp. 899-912
Author(s):  
Özer Talo ◽  
Yurdal Sever
Keyword(s):  
Statistical Convergence ◽  
Metric Spaces ◽  
Closed Sets ◽  
Convergence Of Sequences ◽  
Positive Integers ◽  
The Relationship ◽  
Convergent Sequences

In this paper we extend the concepts of statistical inner and outer limits (as introduced by Talo, Sever and Ba?ar) to I-inner and I-outer limits and give some I-analogue of properties of statistical inner and outer limits for sequences of closed sets in metric spaces, where I is an ideal of subsets of the set N of positive integers. We extend the concept of Kuratowski statistical convergence to Kuratowski I-convergence for a sequence of closed sets and get some properties for Kuratowski I-convergent sequences. Also, we examine the relationship between Kuratowski I-convergence and Hausdorff I-convergence.

scholarly journals On the almost everywhere statistical convergence of sequences of fuzzy numbers

Filomat ◽  
2019 ◽  
Vol 33 (9) ◽  
pp. 2683-2693 ◽  
Author(s):  
Özer Talo
Keyword(s):  
Statistical Convergence ◽  
Fuzzy Numbers ◽  
Almost Everywhere ◽  
Statistical Limit ◽  
Convergence Of Sequences ◽  
Sequences Of Fuzzy Numbers

In this paper, we define the concept of almost everywhere statistical convergence of a sequence of fuzzy numbers and prove that a sequence of fuzzy numbers is almost everywhere statistically convergent if and only if its statistical limit inferior and limit superior are equal. To achieve this result, new representations for statistical limit inferior and limit superior of a sequence of fuzzy numbers are obtained and we show that some properties of statistical limit inferior and limit superior can be easily derived from these representations.

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