scholarly journals Wijsman deferred statistical convergence and Wijsman strong deferred Cesàro convergence of order a of sequences of sets

2021 ◽  
Author(s):  
M. Cagri Yilmazer ◽  
Mikail Et ◽  
Hacer Sengul Kandemir
Keyword(s):  
Statistical Convergence ◽  
Cesaro Convergence

scholarly journals On statistical convergence and strong Cesàro convergence by moduli

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Fernando León-Saavedra ◽  
M. del Carmen Listán-García ◽  
Francisco Javier Pérez Fernández ◽  
María Pilar Romero de la Rosa
Keyword(s):  
Statistical Convergence ◽  
Convergent Sequence ◽  
Modulus Function ◽  
Cesaro Convergence ◽  
Bounded Sequences ◽  
Convergent Sequences

AbstractIn this paper we will establish a result by Connor, Khan and Orhan (Analysis 8:47–63, 1988; Publ. Math. (Debr.) 76:77–88, 2010) in the framework of the statistical convergence and the strong Cesàro convergence defined by a modulus function f. Namely, for every modulus function f, we will prove that a f-strongly Cesàro convergent sequence is always f-statistically convergent and uniformly integrable. The converse of this result is not true even for bounded sequences. We will characterize analytically the modulus functions f for which the converse is true. We will prove that these modulus functions are those for which the statistically convergent sequences are f-statistically convergent, that is, we show that Connor–Khan–Orhan’s result is sharp in this sense.

scholarly journals Some New Observations on Wijsman ℐ 2 -Lacunary Statistical Convergence of Double Set Sequences in Intuitionistic Fuzzy Metric Spaces

2021 ◽  
Vol 2021 ◽  
pp. 1-17
Author(s):  
Ömer Kişi
Keyword(s):  
Statistical Convergence ◽  
Metric Spaces ◽  
Double Sequence ◽  
Fuzzy Metric Spaces ◽  
Fuzzy Metric ◽  
Intuitionistic Fuzzy ◽  
Lacunary Statistical Convergence ◽  
Cesaro Convergence

In this study, we investigate the notions of the Wijsman ℐ 2 -statistical convergence, Wijsman ℐ 2 -lacunary statistical convergence, Wijsman strongly ℐ 2 -lacunary convergence, and Wijsman strongly ℐ 2 -Cesàro convergence of double sequence of sets in the intuitionistic fuzzy metric spaces (briefly, IFMS). Also, we give the notions of Wijsman strongly ℐ 2 ∗ -lacunary convergence, Wijsman strongly ℐ 2 -lacunary Cauchy, and Wijsman strongly ℐ 2 ∗ -lacunary Cauchy set sequence in IFMS and establish noteworthy results.

Some Cesáro-Type quasinormal convergences

2021 ◽  
Vol 30 (1) ◽  
pp. 75-80
Author(s):  
FATIH NURAY
Keyword(s):  
Statistical Convergence ◽  
Inclusion Relations ◽  
Convergence Of Sequences ◽  
Cesaro Convergence

In this paper we introduce the concepts of quasinormal strong Cesaro convergence, quasinormal statistical convergence, lacunary strong quasinormal convergence and lacunary quasinormal statistical convergence of sequences of functions and give some inclusion relations.

scholarly journals Characterizations of a Banach Space through the Strong Lacunary and the Lacunary Statistical Summabilities

Mathematics ◽  
2020 ◽  
Vol 8 (7) ◽  
pp. 1066 ◽  
Author(s):  
Soledad Moreno-Pulido ◽  
Giuseppina Barbieri ◽  
Fernando León-Saavedra ◽  
Francisco Javier Pérez-Fernández ◽  
Antonio Sala-Pérez
Keyword(s):  
Banach Space ◽  
Normed Space ◽  
Statistical Convergence ◽  
Lacunary Statistical Convergence ◽  
Weakly Unconditionally Cauchy Series ◽  
Cauchy Series ◽  
Cesaro Convergence

In this manuscript we characterize the completeness of a normed space through the strong lacunary ( N θ ) and lacunary statistical convergence ( S θ ) of series. A new characterization of weakly unconditionally Cauchy series through N θ and S θ is obtained. We also relate the summability spaces associated with these summabilities with the strong p-Cesàro convergence summability space.

scholarly journals On the Slowly Decreasing Sequences of Fuzzy Numbers

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Özer Talo ◽  
Feyzi Başar
Keyword(s):  
Statistical Convergence ◽  
Fuzzy Numbers ◽  
Tauberian Condition ◽  
Sequences Of Fuzzy Numbers ◽  
Slowly Decreasing Sequences ◽  
Cesaro Convergence

We introduce the slowly decreasing condition for sequences of fuzzy numbers. We prove that this is a Tauberian condition for the statistical convergence and the Cesáro convergence of a sequence of fuzzy numbers.

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.

Evaluation of the statistical convergence of turbulent flow data

2017 ◽  
Author(s):  
Ramon Martins ◽  
Roney Thompson ◽  
Aristeu Silveira Neto ◽  
Gilmar MOMPEAN ◽  
João Rodrigo Andrade
Keyword(s):  
Turbulent Flow ◽  
Statistical Convergence ◽  
Flow Data

On αβ-statistical convergence for sequences of fuzzy mappings and Korovkin type approximation theorem

Filomat ◽  
2017 ◽  
Vol 31 (12) ◽  
pp. 3749-3760 ◽  
Author(s):  
Ali Karaisa ◽  
Uğur Kadak
Keyword(s):  
Statistical Convergence ◽  
Approximation Theorem ◽  
Linear Operators ◽  
Positive Linear Operators ◽  
Bernstein Operator ◽  
Korovkin Type Approximation Theorem ◽  
Type Approximation ◽  
Inclusion Relations ◽  
Prior Investigation

Upon prior investigation on statistical convergence of fuzzy sequences, we study the notion of pointwise ??-statistical convergence of fuzzy mappings of order ?. Also, we establish the concept of strongly ??-summable sequences of fuzzy mappings and investigate some inclusion relations. Further, we get an analogue of Korovkin-type approximation theorem for fuzzy positive linear operators with respect to ??-statistical convergence. Lastly, we apply fuzzy Bernstein operator to construct an example in support of our result.

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