Rough Convergence Research Articles

Rough Convergence of Double Sequences in $n-$Normed Spaces

In this study, we introduced the concepts of rough convergence, rough Cauchy double sequence, and the set of rough limit points of a double sequence, as well as the rough convergence criteria associated with this set in $n$-normed spaces. Later, we proved that this set is both closed and convex. Finally, we presented the relationships between rough convergence and rough Cauchy double sequence in $n$-normed spaces.

On Gradual Borel Summability Method of Rough Convergence of Triple Sequences of Beta Stancu Operators

We define the concept of rough limit set of a triple sequence space of beta Stancu operators of Borel summability of gradual real numbers and obtain the relation between the set of rough limit and the extreme limit points of a triple sequence space of beta Stancu operators of Borel summability method of gradual real numbers. Finally, we investigate some properties of the rough limit set of beta Stancu operators under which Borel summable sequence of gradual real numbers are convergent. Also, we give the results for Borel summability method of series of gradual real numbers.

A Note on Rough Abel Convergence

In this paper, we define a new type of Abel convergence by using the rough convergence of a sequence. We also obtained some results for this convergence.

On rough deferred statistical convergence of difference sequences in [formula omitted]-fuzzy normed spaces

The current article broadly environs the introduction of rough deferred statistical convergence via difference operators as an extension of rough convergence, in the setting of L-fuzzy normed space. The paper also discusses the inevitable limit set of the novel convergence along with the proof of it being convex and closed with regard to the L-fuzzy norm. There is a further establishment of Δrj-deferred statistical cluster point and investigation of relations between the set of cluster points and the aforementioned convergence limit set.

Rough statistical convergence of double sequences in intuitionistic fuzzy normed spaces

This paper proposes rough convergence and rough statistical convergence of a double sequence in intuitionistic fuzzy normed spaces. It then defines the rough statistical limit points and rough statistical cluster points of a double sequence in these spaces. Afterwards, this paper examines some of their basic properties. Finally, it discusses the need for further research.

I-Statistical Rough Convergence of Order α

The aim of this paper is to define the concept of I-statistical (I-st) rough convergence of order α (0 < α ≤ 1). It proposes the concept of I-st bounded of order α. Moreover, the necessary and sufficient condition for a sequence (x_k) to be I-st bounded of order α is studied. In addition, the necessary and sufficient condition for a sequence (x_k) to be I-st convergent of order α is examined. Finally, the need for further research studies is discussed.

Rough I-convergence in cone metric spaces

Here we have studied the notion of rough I-convergence as an extension work of the idea of rough convergence in a cone metric space using ideals. We have further introduced the notion of rough I∗-convergence of sequences in a cone metric space to find the relationship between rough I and I∗-convergence of sequences.

On Rough Convergence of Complex Uncertain Sequences

Complex uncertain variables are measurable functions from an uncertainty space to the set of complex numbers and are used to model complex uncertain quantities. The main purpose of this paper is to introduce rough convergence of complex uncertain sequences and study some convergence concepts namely rough convergence in measure, rough convergence in mean, rough convergence in distribution of complex uncertain sequences. Lastly some relationship between them have been investigated.

On rough convergence in amenable semigroups and some properties

The authors of the present paper, firstly, investigated relations between the notions of rough convergence and classical convergence, and studied on some properties of the rough convergence notion which the set of rough limit points and rough cluster points of a sequence of functions defined on amenable semigroups. Then, they examined the dependence of r-limit LIMrf of a fixed function f ∈ G on varying parameter r.

Rough statistical convergence in intuitionistic fuzzy normed spaces

In this paper, we have defined rough statistical convergence in intuitionistic fuzzy normed spaces which is an useful characterization in the field of statistical convergence. We have proved some properties related to rough convergence which provides some new functional tools in the situation of uncertainty like intuitionistic fuzzy normed spaces. Further, we have established the relationship between the set of statistical limit points and set of cluster points of rough statistically convergent sequences in these spaces.

On the Borel summability method of rough convergence of triple sequences of Bernstein-Stancu operator of fuzzy numbers

On the Borel summability method of rough convergence of triple sequences of Bernstein-Stancu operator of fuzzy numbers

Rough convergence for difference sequences

Rough convergence for difference sequences

On rough convergence of triple sequence space of Bernstein operator of fuzzy numbers defined by a metric

We define the concept of rough limit set of a triple sequence space of Bernstein polynomials of fuzzy numbers and obtain the relation between the set of rough limit and the extreme limit points of a triple sequence space of Bernstein polynomials of fuzzy numbers. Finally, we investigate some properties of the rough limit set of Bernstein polynomials.

ROUGH CONVERGENCE OF DOUBLE SEQUENCES OF FUZZY NUMBERS

In this paper, we define the concepts of rough convergence and rough Cauchy sequence of double sequences of fuzzy numbers. Then, we investigate some relations between rough limit set and extreme limit points of such sequences.

On rough convergence of ρ-Cauchy sequence of triple sequences

Abstract In this paper we define and study rough convergence of triple sequences and the set of rough limit points of a triple sequence. We also investigate the relations between the set of cluster points and the set of rough limit points of Cauchy sequences of triple sequence spaces.

On rough convergence of triple sequence spaces of Bernstein-Stancu operators of fuzzy numbers defined by a metric function

We define the concept of rough limit set of a triple sequence space of Bernstein-Stancu polynomials of fuzzy numbers and obtain the relation between the set of rough limit and the extreme limit points of a triple sequence space of Bernstein-Stancu polynomials of fuzzy numbers. Finally, we investigate some properties of the rough limit set of Bernstein-Stancu polynomials.

L1 of triple sequence sums in six dimensions

In this paper, X.Z. Krasniqi modified trigonometric since sum is extended from one dimensions to three dimensions and the integrability and L1 – rough convergence of triple cosine series under a new class Srst of numerical sequences has been studied.

Rough convergence of sequences in a cone metric space

Here we have introduced the idea of rough convergence of sequences in a cone metric space. Also it has been investigated how far several basic properties of rough convergence as valid in a normed linear space are affected in a cone metric space.

On rough convergence in 2-normed spaces and some properties

In this study, we investigated relationships between rough convergence and classical convergence and studied some properties about the notion of rough convergence, the set of rough limit points and rough cluster points of a sequence in 2-normed space. Also, we examined the dependence of r-limit LIMr 2xn of a fixed sequence (xn) on varying parameter r in 2-normed space

On rough convergence of triple sequence spaces of Bernstein-Stancu operators of fuzzy numbers defined by a metric function

On rough convergence of triple sequence spaces of Bernstein-Stancu operators of fuzzy numbers defined by a metric function