On the convergence and statistical convergence of difference sequences of fractional order

2021 ◽  
Author(s):  
M. Mursaleen ◽  
P. Baliarsingh
Keyword(s):  
Fractional Order ◽  
Statistical Convergence ◽  
Difference Sequences

scholarly journals I−LACUNARY STATISTICAL CONVERGENCE OF ORDER β OF DIFFERENCE SEQUENCES OF FRACTIONAL ORDER

2021 ◽  
pp. 043
Author(s):  
Nazlım Deniz Aral ◽  
Hacer Şengül Kandemir
Keyword(s):  
Fractional Order ◽  
Statistical Convergence ◽  
Difference Sequences ◽  
Lacunary Statistical Convergence

In this paper, we introduce the concepts of ideal ∆α−lacunary statis- tical convergence of order β with the fractional order of α and ideal ∆α−lacunary strongly convergence of order β with the fractional order of α ( where 0 < β ≤ 1and α be a fractional order) and give some relations about these concepts.

On certain spaces of double sequences by de la Vallée-Poussin mean

2015 ◽  
Vol 08 (04) ◽  
pp. 1550079 ◽  
Author(s):  
Kuldip Raj ◽  
Suruchi Pandoh
Keyword(s):  
Statistical Convergence ◽  
Orlicz Function ◽  
Double Difference ◽  
Double Sequences ◽  
Normed Spaces ◽  
Interval Numbers ◽  
Convergence Spaces ◽  
Difference Sequences ◽  
Inclusion Relations ◽  
De La Vallée Poussin

In this paper, we introduce some [Formula: see text]-convergence spaces of double difference sequences of interval numbers with Musielak–Orlicz function [Formula: see text] over [Formula: see text]-normed spaces. We also make an effort to study some topological properties and inclusion relations between these spaces. Furthermore, we study [Formula: see text]-statistical convergence of double difference sequences of interval numbers.

scholarly journals Strongly almost convergent generalized difference sequences associated with multiplier sequences

2007 ◽  
Vol 57 (4) ◽  
Author(s):  
Ayhan Esi ◽  
Binod Tripathy
Keyword(s):  
Statistical Convergence ◽  
Sequence Spaces ◽  
Complex Numbers ◽  
Difference Sequence ◽  
Difference Sequences ◽  
Inclusion Relations ◽  
Difference Sequence Spaces ◽  
Convergent Sequences

AbstractLet Λ = (λk) be a sequence of non-zero complex numbers. In this paper we introduce the strongly almost convergent generalized difference sequence spaces associated with multiplier sequences i.e. w 0[A,Δm,Λ,p], w 1[A,Λm,Λ,p], w ∞[A,Δm,Λ,p] and study their different properties. We also introduce ΔΛm-statistically convergent sequences and give some inclusion relations between w 1[Δm,λ,p] convergence and ΔΛm-statistical convergence.

Statistical Convergence of Order α for Difference Sequences

2015 ◽  
Vol 38 (4) ◽  
pp. 505-514 ◽  
Author(s):  
Y. Altin ◽  
H. Altinok ◽  
R. Çolak
Keyword(s):  
Statistical Convergence ◽  
Difference Sequences
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