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 The backward operator of double almost $\left(\lambda_{m}\mu_{n}\right)$ convergence in $\chi^{2}-$Riesz space defined by a Musielak-Orlicz function

2017 ◽  
Vol 37 (3) ◽  
pp. 85-97
Author(s):  
Nagarajan Subramanian ◽  
Ayhan Esi
Keyword(s):  
Cauchy Sequence ◽  
Statistical Convergence ◽  
Orlicz Function ◽  
Riesz Space

In this paper we introduce the backward operator is $\nabla$ and study the notion of $\nabla-$ statistical convergence and $\nabla-$ statistical Cauchy sequence using by almost $\left(\lambda_{m}\mu_{n}\right)$ convergence in $\chi^{2}-$Riesz space and also some inclusion theorems are discussed.

scholarly journals On generalized statistical convergence and boundedness of Riesz space-valued sequences

Filomat ◽  
2019 ◽  
Vol 33 (15) ◽  
pp. 4989-5002
Author(s):  
Sudip Pal ◽  
Sagar Chakraborty
Keyword(s):  
Statistical Convergence ◽  
Necessary Conditions ◽  
Convergent Sequence ◽  
Bounded Sequence ◽  
Riesz Space ◽  
Riesz Spaces ◽  
Natural Density

We consider the notion of generalized density, namely, the natural density of weight 1 recently introduced in [4] and primarily study some sufficient and almost converse necessary conditions for the generalized statistically convergent sequence under which the subsequence is also generalized statistically convergent. Also we consider similar types of results for the case of generalized statistically bounded sequence. Some results are further obtained in a more general form by using the notion of ideals. The entire investigation is performed in the setting of Riesz spaces extending the recent results in [13].

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.

scholarly journals Weighted lacunary statistical convergence of double sequences in locally solid Riesz spaces

Filomat ◽  
2016 ◽  
Vol 30 (3) ◽  
pp. 621-629
Author(s):  
Şükran Konca
Keyword(s):  
Statistical Convergence ◽  
Riesz Space ◽  
Double Sequences ◽  
Riesz Spaces ◽  
Lacunary Statistical Convergence ◽  
Inclusion Relations ◽  
Locally Solid Riesz Space ◽  
Statistical Boundedness ◽  
Weighted Lacunary Statistical Convergence

Recently, the notion of weighted lacunary statistical convergence is studied in a locally solid Riesz space for single sequences by Ba?ar?r and Konca [7]. In this work, we define and study weighted lacunary statistical ?-convergence, weighted lacunary statistical ?-boundedness of double sequences in locally solid Riesz spaces. We also prove some topological results related to these concepts in the framework of locally solid Riesz spaces and give some inclusion relations.

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 Statistical Convergence of Double Sequences in Locally Solid Riesz Spaces

2012 ◽  
Vol 2012 ◽  
pp. 1-9 ◽  
Author(s):  
S. A. Mohiuddine ◽  
Abdullah Alotaibi ◽  
M. Mursaleen
Keyword(s):  
Statistical Convergence ◽  
Riesz Space ◽  
Double Sequences ◽  
Riesz Spaces ◽  
Locally Solid Riesz Space

Recently, the notion of statistical convergence is studied in a locally solid Riesz space by Albayrak and Pehlivan (2012). In this paper, we define and study statisticalτ-convergence, statisticalτ-Cauchy andS∗(τ)-convergence of double sequences in a locally solid Riesz space.

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.

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