Statistical Equivalent Sequences Research Articles

Asymptotically Lacunary statistical equivalent sequences in partial metric spaces

The present study deals with asymptotically equivalent sequences in partial metric spaces. We define the notions of strongly asymptotically lacunary equivalence, asymptotically statistical equivalence, and asymptotically lacunary statistical equivalence. We theoretically contribute to these notions and investigate some of their basic properties.

I-asymptotically lacunary statistical equivalent sequences in partial metric spaces

The present study deals with I-asymptotically equivalent sequences in partial metric spaces. We define the notions of strongly I-asymptotically lacunary equivalent, I-asymptotically statistical equivalent, and I-asymptotically lacunary statistical equivalent. We theoretically contribute to these notions and investigate some of their basic properties.

On asymptotically deferred statistical equivalent sequences of order $ { \alpha} $ in probability

On asymptotically deferred statistical equivalent sequences of order $ { \alpha} $ in probability

On asymptotically λ-statistical equivalent sequences of order α in probability

In this study, we introduce and examine the concepts of asymptotically ?-statistical equivalent sequences of order ? in probability and strong asymptotically ?-equivalent sequences of order ? in probability. We give some relations connected to these concepts.

On Δm-asymptotically deferred statistical equivalent sequences of order α

In this study we introduce and examine the concepts of ?m-asymptotic deferred statistical equivalence of order ? and strong ?mr-asymptotic deferred equivalence of order ? of sequences of real numbers. Also, we give some relations connected to these concepts.

Asymptotically ideal invariant equivalence

In this paper, the concepts of asymptotically \mathcal{I}_{\sigma}-equivalence, \sigma-asymptotically equivalence, st\-rong\-ly \sigma-asymptotically equivalence and strongly \sigma-asymptotically p-equivalence for real number sequences are de\-fi\-ned. Also, we give relationships among these new type equivalence concepts and the concept of \linebreak S_{\sigma}-asymptotically equivalence which is studied in [Savaş, E. and Patterson, R. F., \sigma-asymptotically lacunary statistical equivalent sequences, Cent. Eur. J. Math., 4 (2006), No. 4, 648–655].

On Asymptotically Lacunary Statistical Equivalent Double Sequences of Fuzzy Numbers

In this paper, we present the asymptotically double lacunary statistical equivalent and strongly asymptotically double lacunary statistical equivalent which is a natural combination of the definition for asymptotically equivalence and lacunary statistical double sequences of fuzzy numbers. In addition, we also give some relations among these new notions.

On almost asymptotically lacunary statistical equivalent sequences induced probabilistic norms

In this paper we study the concept of almost asymptotically lacunary statistical convergent sequences in probabilistic normed spaces and prove some basic properties.

On asymptotically double lacunary statistical equivalent sequences in ideal context

An ideal I is a family of subsets of positive integers N × N which is closed under taking finite unions and subsets of its elements. In this paper, we present some definitions which are a natural combination of the definition of asymptotic equivalence, statistical convergence, lacunary statistical convergence, double sequences and an ideal. In addition, we also present asymptotically I-equivalent double sequences and study some properties of this concept. MSC: 40A35; 40G15

Characterization of asymptotic statistical equivalent double and single sequences

This paper presents a series of four-dimensional matrix characterizations of statistically asymptotically equivalent double and single sequences. These characterizations begins with the presentation of definitions for asymptotically equivalent and asymptotically statistical equivalent of multiple L for double and single sequences. The type of questions we provided answers for are those of the following sort. What are the necessary and sufficient conditions on the entries A that ensure the preservation of statistically asymptotically equivalent rate of convergence.

A generalization on ℐ-asymptotically lacunary statistical equivalent sequences

In this study we extend the concept of ℐ-asymptotically lacunary statistical equivalent sequences by using the sequence which is the sequence of positive real numbers where θ is a lacunary sequence and ℐ is an ideal of the subset of positive integers. MSC:40G15, 40A35.

On ℐ-asymptotically lacunary statistical equivalent sequences

This paper presents the following definition, which is a natural combination of the definitions for asymptotically equivalent, ℐ-statistically limit and ℐ-lacunary statistical convergence. Let θ be a lacunary sequence; the two nonnegative sequences x=( x k ) and y=( y k ) are said to be ℐ-asymptotically lacunary statistical equivalent of multiple L provided that for every ϵ>0, and δ>0, { r ∈ N : 1 h r | { k ∈ I r : | x k y k − L | ≥ ε } | ≥ δ } ∈I (denoted by x ∼ S θ L ( I ) y) and simply ℐ-asymptotically lacunary statistical equivalent if L=1.MSC:40A99, 40A05.

Wijsman Orlicz Asymptotically Ideal -Statistical Equivalent Sequences

An ideal is a family of subsets of positive integers which is closed under taking finite unions and subsets of its elements. In this paper, we introduce a new definition of asymptotically ideal -statistical equivalent sequence in Wijsman sense and present some definitions which are the natural combination of the definition of asymptotic equivalence, statistical equivalent, -statistical equivalent sequences in Wijsman sense. Finally, we introduce the notion of Cesaro Orlicz asymptotically -equivalent sequences in Wijsman sense and establish their relationship with other classes.

On asymptotically generalized statistical equivalent sequences via ideals

For an admissible ideal ${\mathcal I}\subseteq {\mathcal P}({\mathbb N})$ and a non-decreasing realsequence $\lambda =(\lambda_n)$ tending to $\infty$ with $\lambda_{n+1} \leq \lambda_n+1, \lambda_1 = 1$, the objective of this paper is to introduce the new notions ${\mathcal I}-$statistically equivalent, ${\mathcal I}-[V, \lambda]-$equivalent and ${\mathcal I}-\lambda -$statistically equivalent. which are natural combinations of the definitions for asymptotically equivalent, statistical limit, $\lambda-$statistical limit and ${\mathcal I}-$limit for number sequences. In addition, some relations among these new notions are also obtained.

On asymptotically generalized statistical equivalent sequences via ideals

For an admissible ideal ${\mathcal I}\subseteq {\mathcal P}({\mathbb N})$ and a non-decreasing realsequence $\lambda =(\lambda_n)$ tending to $\infty$ with $\lambda_{n+1} \leq \lambda_n+1, \lambda_1 = 1$, the objective of this paper is to introduce the new notions ${\mathcal I}-$statistically equivalent, ${\mathcal I}-[V, \lambda]-$equivalent and ${\mathcal I}-\lambda -$statistically equivalent. which are natural combinations of the definitions for asymptotically equivalent, statistical limit, $\lambda-$statistical limit and ${\mathcal I}-$limit for number sequences. In addition, some relations among these new notions are also obtained.

On Almost Asymptotically Statistical Equivalent Sequences of Fuzzy Numbers

On Almost Asymptotically Statistical Equivalent Sequences of Fuzzy Numbers

On Almost Asymptotically Statistical Equivalent Sequences of Fuzzy Numbers

This paper presents the following definition which is a natural combination of the definitions for almost asymptotically equivalence and almost statistical convergence of fuzzy numbers. Let θ = be a lacunary sequence. The two sequences and of fuzzy numbers are said to be asymptotically θ −statistical equivalent of multiple provided that for every e > 0 lim  ∈ : ! , # ≥ e% = 0, uniformly in & (denoted by ~ (θ) * ) and simply almost asymptotically−statistical equivalent if = 1. Also, we prove that some inclusion relations. 2010 Mathematics Subject Classification. 40A05, 40A35, 40G15, 03E72.

Asymptotically ?-invariant statistical equivalent sequences of fuzzy numbers

This paper presents the following definition which is a natural combination of the definitions for asymptotically equivalent λ-statistical convergence and σ -convergence of fuzzy numbers. Two sequences X and Y of fuzzy numbers are said to be asymptotically λ-invariant statistical equivalent of multiple L provided that for every e> 0, lim n 1 λn k ∈ In : − d X σ k (m) Y σ k(m) , L ≥ e = 0, uniformly in m denoted by X S L ,λ (F) ∼ Y and simply asymptotically λ-invariant statistical equivalent if L = 1.

On Asymptotically -Statistical Equivalent Sequences of Fuzzy Numbers

The goal of this paper is to give the asymptotically -statistical equivalent which is a natural combination of the definition for asymptotically equivalent, invariant mean and -statistical convergence of fuzzy numbers.

σ-asymptotically lacunary statistical equivalent sequences

This paper presents the following definitions which is a natural combination of the definition for asymptotically equivalent, statistically limit, lacunary sequences, and σ-convergence. Let ϑ be a lacunary sequence; Two nonnegative sequences [x] and [y] are S σ,8-asymptotically equivalent of multiple L provided that for every e > 0 $$\mathop {\lim }\limits_r \frac{1}{{h_r }}\left\{ {k \in I_r :\left| {\frac{{x_{\sigma ^k (m)} }}{{y_{\sigma ^k (m)} }} - L} \right| \geqslant \in } \right\} = 0$$ uniformly in m = 1, 2, 3, ..., (denoted by x $$\mathop \sim \limits^{S_{\sigma ,\theta } } $$ y) simply S σ,8-asymptotically equivalent, if L = 1. Using this definition we shall prove S σ,8-asymptotically equivalent analogues of Fridy and Orhan’s theorems in [5] and analogues results of Das and Patel in [1] shall also be presented.