Lacunary Statistical Convergence Of Order Research Articles

Modulated Lacunary 𝒫-Statistical Convergence of Order γ of Sequences of Fuzzy Functions

The central objective of this paper is to investigate the lacunary statistical convergence of order [Formula: see text] and strong lacunary summability of order [Formula: see text] for sequences of fuzzy functions by using the modulus function and a regular matrix. We examine the relevant inclusion relations between these spaces under specific conditions. Additionally, we study properties related to these spaces and establish several interesting results.

Neutrosophic Y-Cesàro summability of a sequence of order α, of neutrosophic random variables in probability

In this paper, we define the notions of neutrosophic $ \mathfrak{Y} $-Ces\`aro summability of a sequence of order $ \alpha $, neutrosophic $ \mathfrak{Y} $-lacunary statistical convergence of order $ \alpha $, neutrosophic strongly $ \mathfrak{Y} $-lacunary statistical convergence of order $ \alpha $ and neutrosophic strongly $ \mathfrak{Y} $-Ces\`aro summability of order $ \alpha $ in neutrosophic probability. Besides, we prove some relations among them.

Some results on lacunary statistical convergence of order $$\alpha$$ in credibility space

Some results on lacunary statistical convergence of order $$\alpha$$ in credibility space

Generalized lacunary statistical convergence of order β of difference sequences of fractional order


 
 
 In this paper, using a modulus function we generalize the concepts of ∆m−lacunary statistical convergence and ∆m−lacunary strongly convergence (m ∈ N) to ∆α−lacunary statistical convergence of order β with the fractional order of α and ∆α−lacunary strongly convergence of order β with the fractional order of α ( where 0 < β ≤ 1 and α be a fractional order).
 
 

(∆mv , f)-lacunary statistical convergence of order α

In this paper, we define the space Sαθ (∆mv, f) of all (∆mv, f)-lacunary statistical convergent sequences of order α with the help of unbounded modulus function f, lacunary sequence (θ), generalized difference operator ∆ mv and real number α ∈ (0, 1]. We also introduce the space ωαθ (∆mv, f) of all strong (∆mv, f)-lacunary summable sequences of order α. Properties related to these spaces are studied. Inclusion relations between spaces Sαθ (∆mv, f) and ωα θ (∆mv, f) are established under certain conditions.

Lacunary statistical convergence of order $$\alpha, \beta$$ for generalized vector-valued difference sequence spaces

In this paper, we defined space $$S_\theta ^{\alpha ,\beta } (\Delta _v^m,E,q)$$ of all vector-valued lacunary $$\Delta _v^m$$ -statistical convergent sequences of order $$(\alpha , \beta )$$ and space $$N_\theta ^{\alpha ,\beta } (\Delta _v^m,E,q,p)$$ of all vector-valued strongly $$\Delta _v^m$$ -lacunary summable sequences of order $$(\alpha ,\beta )$$ by taking sequence $$(E_k, q_k)$$ of normed spaces, where p is a positive real number and $$\alpha ,\beta$$ are real numbers with $$0<\alpha \leqslant \beta \leqslant 1$$ . Some inclusion relations between these spaces are obtained. We also studied space $$\omega _\theta ^{\alpha ,\beta } (\Delta _v^m,f,E,q,p)$$ of all vector-valued strongly $$\Delta _v^m$$ -lacunary summable sequences of order $$(\alpha , \beta )$$ with respect to modulus function f by taking a bounded sequence $$(p_k)$$ of strictly positive real numbers with $$\displaystyle \inf _k p_k>0$$ . The inclusion relations between spaces $$\omega _\theta ^{\alpha ,\beta } (\Delta _v^m,f,E,q,p)$$ and $$S_\theta ^{\alpha ,\beta } (\Delta _v^m,E,q)$$ are determined.

Generalized Difference Sequence Spaces of Fractional Order Defined by Orlicz Functions

The main purpose of this paper is to introduce the concepts of Δ^{α}-lacunary statistical convergence of order β (0<β≤1) with the fractional order of α and Δ^{α}-lacunary strongly convergence of order β (0<β≤1) with the fractional order of α. We establish some connections between Δ^{α}-lacunary strongly convergence of order β and Δ^{α}-lacunary statistical convergence of order β.

(A,φ)-lacunary statistical convergence of order α

In the present paper, we introduce and study (A,?) -statistical convergence of order ?, using the ?-function, infinite matrix and we establish some inclusion theorems.

On (f, I) - Lacunary statistical convergence of Order α of sequences of sets

In this paper we introduce the concepts of Wijsman $% \left( f,I\right) -$lacunary statistical{\Large \ }convergence of order $% \alpha $ and Wijsman strongly $\left( f,I\right) -$lacunary statistical% {\Large \ }convergence of order $\alpha ,$ and investigated between their relationship.

$\mathcal{I}$-Cesaro Summability of a Sequence of Order $\alpha$ of Random Variables in Probability

In this paper, we define four types of convergence of a sequence of random variables, namely, $\mathcal{I}$-statistical convergence of order $ \alpha $, $\mathcal{I}$-lacunary statistical convergence of order $\alpha $, strongly $\mathcal{I}$-lacunary convergence of order $\alpha $ and strongly $ \mathcal{I}$-Cesaro summability of order $\alpha $ in probability where $ 0&amp;lt;\alpha &amp;lt;1$. We establish the connection between these notions.

Double Lacunary Statistical Convergence of Order \(\alpha\) in Topological Groups via Ideal

Recently, \(\mathcal{I}\)-lacunary double statistical convergence in topological groups is presented by Savas [31]. In this paper, we extend the concepts of \(\mathcal{I}\)-double statistical convergence and \(\mathcal{I}\)-double lacunary statistical convergence to the concepts of \(\mathcal{I}\)-double statistical convergence and \(\mathcal{I}\)-double lacunary statistical convergence of order \(\alpha\), \(0 <\alpha \leq 1\). We also investigate some inclusion relations between \(\mathcal{I}\)-double statistical of order \(\alpha\) and \(\mathcal{I}\)-double lacunary double statistical convergence of order \(\alpha\).

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

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.

Lacunary statistical convergence and strongly lacunary summable functions of order α

The main purpose of this paper is to introduce and investigate the concepts of lacunary strong summability of order  and lacunary statistical convergence of order  of real-valued functions which are measurable (in the Lebesgue sense) in the interval (1,∞). Some relations between lacunary statistical convergence of order  and lacunary strong summability of order  are also given.

Lacunary statistical convergence of order (α, β) in topological groups

In this paper, the concept of lacunary statistical convergence of order (α, β) is generalized to topological groups, and some inclusion relations between the set of all statistically convergent sequences of order (α, β) and the set of all lacunary statistically convergent sequences of order (α, β) are given.

Some Cesàro-type summability spaces defined by a modulus function of order (α;β)

In this article, we introduce strong w [ ; f; p] summability of order (α;β) for sequences of complex (or real) numbers and give some inclusionrelations between the sets of lacunary statistical convergence of order (α;β) strong w [ ; f; p]summability and strong w (p)summability

Lacunary statistical convergence of order β in difference sequences of fuzzy numbers

In this paper, we define the spaces N β θ (p, F, � m ) ,S β (F, � m ) ,w β (F, � m ) for sequences of fuzzy numbers using generalized difference operatorm and a lacunary sequence θ and give some relations between them, where β ∈ (0, 1) and p> 0. Furthermore, in the last section of paper, some inclusion theorems are presented related to the spaces S β θ (F, � m ) and w β (θ, f, F, � m ) according to modulus function f .

On Pointwise Lacunary Statistical Convergence of Order α of Sequences of Function

In this paper we introduce the concepts of pointwise lacunary statistical convergence of order α and pointwise \(w_{p}(f,\theta )\)—summability of order α of sequences of real valued functions. Also some relations between pointwise \(S_{\theta }^{\alpha }(f)\)—statistical convergence and pointwise \(w_{p}^{\alpha }(f,\theta )\)—summability are given.

On lacunary statistical convergence of order α

In this article, we introduce the concept of lacunary statistical convergence of order α of real number sequences and give some inclusion relations between the sets of lacunary statistical convergence of order α and strong Nθα(p)-summability. Furthermore, some relations between the spaces NθαSθα are examined.

Some Cesaro-type summability spaces of order α and lacunary statistical convergence of order α

In the paper [32], we have defined the concepts of lacunary statistical convergence of order ? and strong N?(p)-summability of order ? for sequences of complex (or real) numbers. In this paper we continue to examine others relations between lacunary statistical convergence of order ? and strong N?(p)-summability of order ?.

Double almost lacunary statistical convergence of order α

In this paper, we define and study lacunary double almost statistical convergence of order α. Further, some inclusion relations have been examined. We also introduce a new sequence space by combining lacunary double almost statistical convergence and Orlicz function.MSC:40B05, 40C05.