On Triple Sequence Spaces of Bernstein Operator of χ3 of Rough λ-Statistical Convergence in Probability of Random Variables Defined by Musielak-Orlicz Function

2018 ◽  
Vol 11 (2) ◽  
pp. 62-70 ◽  
Author(s):  
A. Esi ◽  
N. Subramanian
Keyword(s):  
Statistical Convergence ◽  
Orlicz Function ◽  
Random Variables ◽  
Sequence Spaces ◽  
Convergence In Probability ◽  
Bernstein Operator

scholarly journals On some double almost lacunary sequence spaces defined by Orlicz functions

Filomat ◽  
2005 ◽  
pp. 35-44 ◽  
Author(s):  
Ekrem Savas ◽  
Richard Patterson
Keyword(s):  
Sequence Space ◽  
Statistical Convergence ◽  
Orlicz Function ◽  
Lacunary Sequence ◽  
Sequence Spaces ◽  
Double Sequences ◽  
Orlicz Functions ◽  
Lacunary Statistical Convergence

In this paper we introduce a new concept for almost lacunary strong P-convergent with respect to an Orlicz function and examine some properties of the resulting sequence space. We also introduce and study almost lacunary statistical convergence for double sequences and we shall also present some inclusion theorems.

scholarly journals Riesz almost lacunary multiple triple sequence spaces of $\Gamma^{3}$ defined by a Musielak-Orlicz function

2018 ◽  
Vol 37 (4) ◽  
pp. 47-59
Author(s):  
N. Subramanian ◽  
N. Rajagopal ◽  
P. Thirunavukarasu
Keyword(s):  
Statistical Convergence ◽  
Orlicz Function ◽  
Sequence Spaces

In this paper we introduce a new concept for Riesz almost lacunary $\Gamma^{3}$ sequence spaces strong $P-$ convergent to zero with respect to an Musielak-Orlicz function and examine some properties of the resulting sequence spaces. We also introduce and study statistical convergence of Riesz almost lacunary $\Gamma^{3}$ sequence spaces and also some inclusion theorems are discussed.

Bernstein Operator of Rough λ-statistically and ρ Cauchy Sequences Convergence on Triple Sequence Spaces

2018 ◽  
Vol 85 (1-2) ◽  
pp. 256 ◽  
Author(s):  
S. Velmurugan ◽  
N. Subramanian
Keyword(s):  
Statistical Convergence ◽  
Bernstein Polynomials ◽  
Sequence Spaces ◽  
Bernstein Operator ◽  
Convergence Criteria ◽  
Statistical Limit ◽  
Cauchy Sequences ◽  
Natural Density ◽  
Limit Points

<p>In this article, using the concept of natural density, we introduce the notion of Bernstein polynomials of rough λ−statistically and ρ−Cauchy triple sequence spaces. We define the set of Bernstein polynomials of rough statistical limit points of a triple sequence spaces and obtain to λ−statistical convergence criteria associated with this set. We examine the relation between the set of Bernstein polynomials of rough λ−statistically and ρ− Cauchy triple sequences.</p><p> </p><p> </p>

Almost strongly Orlicz double sequence spaces of regular matrices and their applications to statistical convergence

2018 ◽  
Vol 11 (05) ◽  
pp. 1850073 ◽  
Author(s):  
Kuldip Raj ◽  
Anu Choudhary ◽  
Charu Sharma
Keyword(s):  
Statistical Convergence ◽  
Orlicz Function ◽  
Double Sequence ◽  
Convergent Sequence ◽  
Sequence Spaces ◽  
Regular Matrix ◽  
Normed Spaces ◽  
Double Sequence Spaces ◽  
Inclusion Relations ◽  
Algebraic Properties

In this paper, we introduce and study some strongly almost convergent double sequence spaces by Riesz mean associated with four-dimensional bounded regular matrix and a Musielak–Orlicz function over [Formula: see text]-normed spaces. We make an effort to study some topological and algebraic properties of these sequence spaces. We also study some inclusion relations between the spaces. Finally, we establish some relation between weighted lacunary statistical sequence spaces and Riesz lacunary almost statistical convergent sequence spaces over [Formula: see text]-normed spaces.

scholarly journals Some Seminormed Difference Sequence Spaces over n-Normed Spaces Defined by a Musielak-Orlicz Function of Order (α,β)

2018 ◽  
Vol 2018 ◽  
pp. 1-11 ◽  
Author(s):  
S. A. Mohiuddine ◽  
Sunil K. Sharma ◽  
Dina A. Abuzaid
Keyword(s):  
Statistical Convergence ◽  
Orlicz Function ◽  
Sequence Spaces ◽  
Difference Sequence ◽  
Topological Properties ◽  
Normed Spaces ◽  
Lacunary Statistical Convergence ◽  
Inclusion Relations ◽  
Difference Sequence Spaces

We first define the notion of lacunary statistical convergence of order (α,β), and taking this notion into consideration, we introduce some seminormed difference sequence spaces over n-normed spaces with the help of Musielak-Orlicz function M=(Mk) of order (α,β). We also examine some topological properties and prove inclusion relations between the resulting sequence spaces.

scholarly journals Triple Almost (λ_{m_{i}}μ_{n_{ℓ}}γ_{k_{j}}) Lacunary Riesz χ_{R_{λ_{m_{i}}μ_{n_{ℓ}}γ_{k_{j}}}}³ sequence spaces defined by Orlicz function

2017 ◽  
Vol 37 (2) ◽  
pp. 129-144
Author(s):  
Nagarajan Subramanian ◽  
Ayhan Esi
Keyword(s):  
Statistical Convergence ◽  
Orlicz Function ◽  
Riesz Space ◽  
Sequence Spaces ◽  
Riesz Spaces

In this paper we introduce a new concept for generalized almost (λ_{m_{i}}μ_{n_{ℓ}}γ_{k_{j}}) convergence in χ_{R_{λ_{m_{i}}μ_{n_{ℓ}}γ_{k_{j}}}}³-Riesz spaces strong P- convergent to zero with respect to an Orlicz function and examine some properties of the resulting sequence spaces. We also introduce and study statistical convergence of generalized almost (λ_{m_{i}}μ_{n_{ℓ}}γ_{k_{j}}) convergence in χ_{R_{λ_{m_{i}}μ_{n_{ℓ}}γ_{k_{j}}}}³-Riesz space and also some inclusion theorems are discussed.

scholarly journals On Some New Sequence Spaces and Statistical Convergence Methods for Double Sequences

2014 ◽  
Vol 47 (3) ◽  
Author(s):  
Cemal Belen ◽  
Mustafa Yildirim
Keyword(s):  
Statistical Convergence ◽  
Orlicz Function ◽  
Double Sequence ◽  
Sequence Spaces ◽  
Double Sequences ◽  
Double Sequence Spaces ◽  
Lacunary Statistical Convergence

AbstractIn this paper, we introduce some new double sequence spaces with respect to an Orlicz function and define two new convergence methods related to the concepts of statistical convergence and lacunary statistical convergence for double sequences. We also present some inclusion theorems for our newly defined sequence spaces and statistical convergence methods

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