Ideal Convergent Sequences Research Articles

Characterization of lacunary ℐ-convergent sequences in credibility space

Abstract This research paper aims to introduce the concept of lacunary ideal Cauchy sequences of fuzzy variables in a credibility space. We establish the interrelationships between this notion with lacunary ideal convergent sequences in the same structure from several aspects of credibility. Furthermore, we explore the concepts of strongly lacunary Cauchy, strongly ℐ {\mathcal{I}} -lacunary Cauchy, and strongly ℐ ∗ {\mathcal{I}^{\ast}} -lacunary Cauchy sequences of fuzzy variables within the context of credibility. We also examine the interconnections between these concepts and analyze their relationships.

ROUGH IDEAL CONVERGENT SEQUENCE SPACES OF BOUNDED LINEAR OPERATORS

In this paper, using the concept of rough ideal convergence in normedlinear spaces, we introduce rough ideal convergence for bounded linear operators.We also introduce some rough ideal convergent sequence spaces of bounded linearoperators and further investigate and study some inclusion relations of these spaces,decomposition theorem and algebraic properties.

Riesz ideal convergence in neutrosophic normed spaces

In this paper, we define concept of ideal(I) convergent sequences as a domain of regular Riesz triangular matrix and also using neutrosophic normed space. In neutrosophic normed spaces, we describe the idea of a generalization of the Riesz ideal convergence and the Riesz Cauchy sequence, and we also show certain aspects of these ideas. Finally, we define the concept of I∗-convergence in neutrosophic normed space and show that it is related to Riesz I-convergence in neutrosophic normed space. Moreover, we clearly show some results related to these theories and provide counterexamples.

On the Ideal Convergent Sequences in Fuzzy Normed Space

This article discusses a variety of important notions, including ideal convergence and ideal Cauchyness of topological sequences produced by fuzzy normed spaces. Furthermore, the connections between the concepts of the ideal limit and ideal cluster points of a sequence in a fuzzy normed linear space are investigated. In a fuzzy normed space, we investigated additional effects, such as describing compactness in terms of ideal cluster points and other relevant but previously unresearched ideal convergence and adjoint ideal convergence aspects of sequences and nets. The countable compactness of a fuzzy normed space and its link to it were also defined. The terms ideal and its adjoint divergent sequences are then introduced, and specific aspects of them are explored in a fuzzy normed space. Our study supports the importance of condition (AP) in examining summability via ideals. It is suggested to use a fuzzy point symmetry-based genetic clustering method to automatically count the number of clusters in a data set and determine how well the data are fuzzy partitioned. As long as the clusters have the attribute of symmetry, they can be any size, form, or convexity. One of the crucial ways that symmetry is used in fuzzy systems is in the solution of the linear Fuzzy Fredholm Integral Equation (FFIE), which has symmetric triangular (Fuzzy Interval) output and any fuzzy function input.

An investigation on the triple ideal convergent sequences in fuzzy metric spaces

The notion of ideal convergence is a process of generalizing of statistical convergence which is dependent on the idea of the ideal $I$ of subsets of the set positive integer numbers. In this study we also present the concept of ideal convergence for triple sequences in fuzzy metric spaces (FMS) in the manner of George and Veeramani and the terms of ideal Cauchy sequence and $I^{∗}$-Cauchy sequence in FMS and study their certain properties.

SPACES OF FIBONACCI DIFFERENCE IDEAL CONVERGENT SEQUENCES IN RANDOM 2–NORMED SPACE

In this article, by using Fibonacci difference matrix F and the notion of ideal convergence of sequences in random 2–normed space, we introduce some new spaces of Fibonacci difference ideal convergent sequences with respect to random 2 -norm and study some inclusion relations, topological and algebraic properties of these spaces.

Ideal convergent sequences of functions in probabilistic normed spaces

In the present article, we have defined the notion of \(I\)-pointwise convergence and \(I\)-uniform convergence of sequence of functions defined on a probabilistic normed space with respect to the probabilistic norm \(\nu\). Further we have given the Cauchy criteria for \(I\)-pointwise and \(I\)-uniform convergence in PNS. Also, we have proved certain results on continuity of functions with respect to \(\nu\) in PNS.

On paranormed Ideal convergent sequence spaces defined by Jordan totient function

The study of sequence spaces and summability theory has been an important aspect in defining new notions of convergence for the sequences that do not converge in the usual sense. Paving the way into the applications of law of large numbers and theory of functions, it has proved to be an essential tool. In this paper we generalise the classical Maddox sequence spaces c_{0}(p), c(p), ell (p) and ell _{infty }(p) and define new ideal paranormed sequence spaces c^{I}_{0}(Upsilon ^{r}, p), c^{I}(Upsilon ^{r}, p), ell ^{I}_{ infty }(Upsilon ^{r}, p) and ell _{infty }(Upsilon ^{r}, p) defined with the aid of Jordan’s totient function and a bounded sequence of positive real numbers. We develop isomorphism between certain maps and also find their α-, β- and γ-duals. We examine algebraic and topological properties of these corresponding spaces. Further we study some standard inclusion relations and prove the decomposition theorem.

A study of Nörlund ideal convergent sequence spaces

The N?rlund matrix Nt in the theory of sequence space was firstly used by Wang. In this paper, by using the N?rlund mean Nt and the notion of ideal convergence, we introduce some new sequence spaces cI 0(Nt), cI (Nt), and lI?(Nt) as a domain of N?rlund mean. We study some topological and algebraic properties on these spaces. Further, some inclusion concerning these spaces are discussed.

Ideal convergent sequence spaces of fuzzy star–shaped numbers

In 1990, Diamond [16] primarily established the base of fuzzy star–shaped sets, an extension of fuzzy sets and numerous of its properties. In this paper, we aim to generalize the convergence induced by an ideal defined on natural numbers ℕ , introduce new sequence spaces of fuzzy star–shaped numbers in ℝ n and examine various algebraic and topological properties of the new corresponding spaces as well. In support of our results, we provide several examples of these new resulting sequences.

On Properties of Ideal Convergent Sequences in Jordan Intuitionistic Fuzzy Normed Spaces

On Properties of Ideal Convergent Sequences in Jordan Intuitionistic Fuzzy Normed Spaces

On some (Cλ, 1)(Eλ, q) ideal convergent sequence spaces

On some (Cλ, 1)(Eλ, q) ideal convergent sequence spaces

Some Results on Strongly Cesáro Ideal Convergent Sequence Spaces

Some algebraic properties of Cesáro ideal convergent sequence spaces, C I and C 0 I , are studied in this article and some inclusion relations on these spaces are established.

Some ideal convergent multiplier sequence spaces using de la Vallee Poussin mean and Zweier operator

We introduce multiplier type ideal convergent sequence spaces, using Zweier transform and de la Vallee Poussin mean. We study some topological and algebraic properties of these spaces. Further we prove some inclusion relations related to these spaces.

On Generalized Difference Ideal Convergence in Generalized Probabilistic n-normed Spaces

In this article, we introduce the concept of $$\varDelta ^{m}-I$$ -convergent and $$\varDelta ^{m}-I$$ Cauchy sequences in generalized probabilistic n-normed spaces and establish some results relating to this concept. We also study $$\varDelta ^{m}-I^{*}$$ convergence in the same space. Statement Probabilistic norm generalizes and unifies different notions of norm, represented by a distance function, rather than a positive real number. Ideal convergence unifies many notions of convergence of sequences. In this article, we have introduced the notion of generalized difference ideal convergent sequences in probabilistic n-normed space, which generalizes and unifies many existing notions. Hence, the results of this article have been established in general setting.

On some results in intuitionistic fuzzy ideal convergence double sequence spaces

Recently, spaces of ideal convergent sequences of bounded linear operators were studied by Khan et al. (Numer. Funct. Anal. Optim. 39:1278-1290, 2018). This has motivated us to propose the intuitionistic fuzzy I-convergent double sequence spaces determined by the bounded linear operator. In this paper, we investigate the algebraic and topological properties. We also study the concept of the ideal Cauchy and ideal convergence on the said spaces.

Matrix transformations related to I-convergent sequences

Characterized are matrix transformations related to certain subsets of the space of ideal convergent sequences. Obtained here results are connected with the previous investigations of the author on some transformations defined by infinite matrices of bounded linear operators.

A Letter Concerning Leonetti’s Paper ‘Continuous Projections Onto Ideal Convergent Sequences’

Leonetti proved that whenever $${\mathcal {I}}$$ is an ideal on $${\mathbb {N}}$$ such that there exists an uncountable family of sets that are not in $${\mathcal {I}}$$ with the property that the intersection of any two distinct members of that family is in $${\mathcal {I}}$$ , then the space $$c_{0,{\mathcal {I}}}$$ of sequences in $$\ell _\infty $$ that converge to 0 along $${\mathcal {I}}$$ is not complemented. We provide a shorter proof of a more general fact that the quotient space $$\ell _\infty / c_{0,{\mathcal {I}}}$$ does not even embed into $$\ell _\infty $$ .

On fuzzy valued lacunary ideal convergent sequence spaces defined by a compact operator

On fuzzy valued lacunary ideal convergent sequence spaces defined by a compact operator

Spaces of Ideal Convergent Sequences of Bounded Linear Operators

The notation of I–convergence was introduced and studied by Kostyrko, Macaj, Salat, and Wilczynski. Recently, the concept of I–convergent for a sequence of bounded linear operators has been studied by Khan and Shafiq. This has motivated us to introduce and study some new spaces of double sequences of bounded linear operators and their basic topological and algebraic properties of these spaces. And we study some of their basic topological and algebraic properties of these spaces. We prove some inclusion relations on these spaces.