Statistical Convergence Of Order Research Articles

On (λ, I)-Statistical Convergence of Order α of Sequences of Function

In this paper, we introduce the concepts of pointwise (λ, I)-statistical convergence of order α and pointwise w p (λ, I)-summability of order α. Also some relations between pointwise (λ, I)-statistical convergence of order α and pointwise w p (λ, I)-summability of order α are given.

F_{(lambda,mu)}-statistical convergence of order \u03b1\u0303 for double sequences

New concepts of f_{lambda,mu }-statistical convergence for double sequences of order α̃ and strong f_{lambda,mu }-Cesàro summability for double sequences of order α̃ are introduced for sequences of (complex or real) numbers. Furthermore, we give the relationship between the spaces w_{tilde{alpha },0}^{2} ( f,lambda,mu ), w_{tilde{alpha }}^{2} ( f,lambda,mu ) and w_{tilde{alpha},infty }^{2} ( f,lambda,mu ). Then we express the properties of strong f_{lambda,mu }-Cesàro summability of order β̃ which is related to strong f_{lambda,mu }-Cesàro summability of order α̃. Also, some relations between f_{lambda,mu }-statistical convergence of order α̃ and strong f_{lambda,mu }-Cesàro summability of order α̃ are given.

Wijsman Rough λ Statistical Convergence of Order α of Triple Sequence of Functions

In this paper, using the concept of natural density, we introduce the notion of Wijsman rough λ statistical convergence of order α triple sequence of functions. We define the set of Wijsman rough λ statistical convergence of order α of limit points of a triple sequence spaces of functions and obtain Wijsman λ statistical convergence of order α criteria associated with this set. Later, we prove that this set is closed and convex and also examine the relations between the set of Wijsman rough λ statistical convergence of order α of cluster points and the set of Wijsman rough λ statistical convergence of order α limit points of a triple sequences of functions.

Iλ-statistically convergent functions of order α

In present paper, we further generalize the recently introduced summability method of [22] and introduce the new notion namely, I?-statistical convergence of order ? for a real valued function which is measurable in the interval (1,?). We mainly investigate certain properties of this convergence. The study leaves some interesting open problems.

Iλ -Statistical Convergence of Order α in Topological Groups

Iλ -Statistical Convergence of Order α in Topological Groups

On Generalized Double Statistical Convergence of Order α in Intuitionistic Fuzzy Normed Spaces

Our goal in this work is to introduce the notion V , λ ( I ) 2 -summability and ideal λ-double statistical convergence of order α with respect to the intuitionistic fuzzy norm μ , v . We also make some observations about these spaces and prove some inclusion relations.

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 .

Some characterizations on weighted $$\beta \gamma $$ β γ -statistical convergence of fuzzy functions of order $$\theta $$ θ

Based on the concept of new type of statistical convergence defined by Aktuglu, we have introduced the weighted $\alpha\beta$ - statistical convergence of order $\theta$ in case of fuzzy functions and classified it into pointwise, uniform and equi-statistical convergence. We have checked some basic properties and then the convergence are investigated in terms of their $\alpha$-cuts. The interrelation among them are also established. We have also proved that continuity, boundedness etc are preserved in the equi-statistical sense under some suitable conditions, but not in pointwise sense.

New type of Lacunary Orlicz difference sequence spaces generated by infinite matrices

The main purpose of this paper is to introduce the spaces ?o? [A,M,?, p] and ?? [A,M,?,p] and ???[A,M,?,p] generated by infinite matrices defined by Orlicz functions. Some properties of these spaces are discussed. Also we introduce the concept of ?? [A,?]-statistical convergence and derive some results between the spaces ?? [A,?] and ??[A,?]. Further, we study some geometrical properties such as order continuous, the Fatou property and the Banach-Saks property of the new space ???? [A,?,p]. Finally, we introduce the notion of ??[A,?]-statistical convergence of order ? of real number sequences and obtain some inclusion relations between the set of ?[A,?]-statistical convergence of order ?.

F-Statistical convergence of order α and strong Cesàro summability of order α with respect to a modulus

In this paper, following a very recent and new approach of Aizpuru et al. (Quaest. Math. 37:525-530, 2014), we further generalize a concept of α-density to that of f α $f_{\alpha}$ -density, where f is an unbounded modulus and 0 < α ≤ 1 $0 < \alpha\leq1$ . As a consequence, we obtain a new nonmatrix convergence method, namely f-statistical convergence of order α or S α f $S_{\alpha}^{f}$ -convergence, which is intermediate between the ordinary convergence and the statistical convergence of order α. We also introduce a new concept of strong Cesaro summability of order α with respect to a modulus function f, and finally we investigate the relationship between the set S α f $S_{\alpha}^{f}$ of all f-statistically convergent sequences of order α and the set w α f $w_{\alpha}^{f}$ of all strongly Cesaro summable sequences of order α with respect to f.

On $$\left( \Delta _{{\uplambda } }^{m},I\right) $$ Δ λ m , I –statistical convergence of order $$\alpha $$ α

In this paper we introduce the concepts of $$\left( \Delta _{{\uplambda } }^{m},I\right) $$ -statistical convergence of order $$\alpha $$ and $$\left[ {V}\right] _{p}\left( \Delta _{{\uplambda } }^{m},I\right) $$ -summability of order $$\alpha $$ of real sequences and investigated between their relationship.

Statistical Convergence of Order α for Difference Sequences

In this paper the concepts of ∆mv-statistical convergence of order α and strong (p, ∆m)-Ces`aro summability of order α are introduced for sequences of complex (or real) numbers. Some relations between the ∆mv-statistical convergence of order α and strong (p, ∆mv)-Ces`aro summability of order α are given. Also some relations between the space ωαp (∆mv, f) and Sα (∆mv) are examined.

Almost statistical convergence of order $$\beta $$ β of sequences of fuzzy numbers

In this article, we introduce the concepts of almost $$\lambda $$ź-statistical convergence of order $$\beta $$β and strongly almost $$\lambda _{p}$$źp-summability of order $$\beta $$β for sequences of fuzzy numbers. Also, we establish some relations between the almost $$\lambda $$ź-statistical convergence of order $$\beta $$β and strongly almost $$\lambda _{p}$$źp-summability of order $$\beta $$β and we define $$\hat{w}_{\lambda }^{\beta }\left( \mathcal {F},f,p\right) $$w^źβF,f,p, where $$f$$f is a modulus function and give some inclusion relations.

Weighted statistical convergence of order α and its applications

Abstract The definition of weighted statistical convergence was first introduced by Karakaya and Chishti (2009) [1]. After that the definition was modified by Mursaleen et al. (2012) [2]. But some problems are still there; so it will be further modified in this paper. Using it some newly developed definitions of the convergence of a sequence of random variables in probability have been introduced and their interrelations also have been investigated, and in this way a partial answer to an open problem posed by Das and Savas (2014) [3] has been given.

Korovkin type approximation theorems for weighted $$\alpha \beta $$ α β -statistical convergence

The concept of $$\alpha \beta $$ -statistical convergence was introduced and studied by Aktuğlu (Korovkin type approximation theorems proved via $$\alpha \beta $$ -statistical convergence, J Comput Appl Math 259:174–181, 2014). In this work, we generalize the concept of $$\alpha \beta $$ -statistical convergence and introduce the concept of weighted $$\alpha \beta $$ -statistical convergence of order $$\gamma $$ , weighted $$\alpha \beta $$ -summability of order $$\gamma $$ , and strongly weighted $$\alpha \beta $$ -summable sequences of order $$\gamma $$ . We also establish some inclusion relation, and some related results for these new summability methods. Furthermore, we prove Korovkin type approximation theorems through weighted $$\alpha \beta $$ -statistical convergence and apply the classical Bernstein operator to construct an example in support of our result.

On $\Lambda$-statistical convergence of order $\alpha$ in random 2-normed space

On $\Lambda$-statistical convergence of order $\alpha$ in random 2-normed space

Statistical convergence of order [formula omitted] in probability

In this paper the ideas of different types of convergence of a sequence of random variables in probability, namely, statistical convergence of order α in probability, strong p-Cesàro summability of order α in probability, lacunary statistical convergence or Sθ-convergence of order α in probability, and Nθ-convergence of order α in probability have been introduced and their certain basic properties have been studied.

On generalized statistical convergence of order β of sequences of fuzzy numbers

In this article we introduce the concepts of $\Delta_{\lambda}^{m}-$statistical convergence of order β and strong $\Delta_{\lambda_{p}}^{m}-$summability of order β for sequences of fuzzy numbers. Also, we establish some relations between the $\Delta_{\lambda}^{m}-$statistical convergence of order β and strong $\Delta_{\lambda_{p}}^{m}-$summability of order β and we define $w_{\lambda}^{\beta}\left\Delta^{m},\mathcal{F},f,p\right$, where $f$ is a modulus function and give some inclusion relations.

On pointwise λ-statistical convergence of order α of sequences of fuzzy mappings

In this study, we introduce the concepts of pointwise ?-statistical convergence of order ? of sequences of fuzzy mappings and strongly pointwise (V,?,p) summable of order ? of sequences of fuzzy mappings. Some relations between pointwise ?-statistical convergence of order ? and strongly pointwise (V,?,p) summable of order ? of sequences of fuzzy mappings are given.

Statistical convergence of order β for generalized difference sequences of fuzzy numbers

In this study we introduce the concepts of Δm-statistical convergence of order β and strong $\Delta_{p}^{m}$-Cesaro summability of order β for sequences of fuzzy numbers by helping many examples. Also, we establish some properties which are valid for sequences of real numbers, but not for sequences of fuzzy numbers.