Lacunary Convergence Research Articles

Almost lacunary statistical and strongly almost lacunary convergence of order (β,γ) of sequences of fuzzy numbers

The main purpose of this article is to introduce the concepts of almost lacunary statistical convergence and strongly almost lacunary convergence of order (β,γ) of sequences of fuzzy numbers with respect to an Orlicz function. We give some relations between strongly almost lacunary convergence and almost lacunary statistical convergence of order (β,γ) of sequences of fuzzy numbers, where β and γ are two fixed real numbers such that 0 β≤γ≤1.

Further Results on Lacunary Difference Sequences of Complex Uncertain Variables in 2-Normed Spaces

A novel approach combining the difference operator on sequence spaces and uncertainty theory has been utilized to establish a fresh class of lacunary convergent difference sequences involving complex uncertain variables in 2-normed spaces. This newly introduced class demonstrates remarkable properties related to lacunary convergence. Additionally, the sequence spaces defined in this context have been thoroughly explored, revealing interesting topological characteristics and valuable insights into inclusion relations. This study offers a rejuvenated perspective on lacunary convergence and its associated concepts through the integration of difference operators and uncertainty theory.

Strongly lacunary convergence of order β of difference sequences of fractional order in neutrosophic normed spaces

Strongly lacunary convergence of order β of difference sequences of fractional order in neutrosophic normed spaces

I-convergent triple fuzzy normed spaces

In this paper we introduce the concept of lacunary ideal convergence of triple sequences in fuzzy normed spaces and the relation between lacunary convergence and lacunary ideal convergence is investigated for triple sequences in fuzzy normed spaces. Concept of limit point and cluster point for triple sequences in fuzzy normed spaces and theorems related to these concepts are also given.

Fibonacci Lacunary Ideal Convergence of Double Sequences in Intuitionistic Fuzzy Normed Linear Spaces

The purpose of this article is to research the concept of Fibonacci lacunary ideal convergence of double sequences in intuitionistic fuzzy normed linear spaces (IFNS). Additionally, a new concept, called Fibonacci lacunary convergence, is examined. Also, Fibonacci lacunary I₂-limit points and Fibonacci lacunary I₂-cluster points for double sequences in IFNS have been defined and the significant results have been given. Additionally, Fibonacci lacunary Cauchy and Fibonacci lacunary I₂-Cauchy double sequences are worked.

Some New Observations on Wijsman ℐ 2 -Lacunary Statistical Convergence of Double Set Sequences in Intuitionistic Fuzzy Metric Spaces

In this study, we investigate the notions of the Wijsman ℐ 2 -statistical convergence, Wijsman ℐ 2 -lacunary statistical convergence, Wijsman strongly ℐ 2 -lacunary convergence, and Wijsman strongly ℐ 2 -Cesàro convergence of double sequence of sets in the intuitionistic fuzzy metric spaces (briefly, IFMS). Also, we give the notions of Wijsman strongly ℐ 2 ∗ -lacunary convergence, Wijsman strongly ℐ 2 -lacunary Cauchy, and Wijsman strongly ℐ 2 ∗ -lacunary Cauchy set sequence in IFMS and establish noteworthy results.

Lacunary Convergence of Double Sequences of Complex Uncertain Variables

In this paper, we introduce the notion of lacunary convergence for double sequences of complex uncertain variables. We have established the relation between lacunary convergence and strong Cesàro convergence. Also, we have established the relation between different concepts of lacunary convergence of double sequences of complex uncertain variables.

On $\mathcal{I}_{\theta }$-convergence in Neutrosophic Normed Spaces

The purpose of this article is to investigate lacunary ideal convergence of sequences in neutrosophic normed space (NNS). Also, an original notion, named lacunary convergence of sequence in NNS, is defined. Also, lacunary $% \mathcal{I}$-limit points and lacunary $\mathcal{I}$-cluster points of sequences in NNS have been examined. Furthermore, lacunary Cauchy and lacunary $\mathcal{I}$-Cauchy sequences in NNS are introduced and some properties of these notions are studied.

Lacunary sequences of complex uncertain variables defined by Orlicz functions

Using the concept of Orlicz function and uncertainty theory, some new class of lacunary convergent sequences defined by Orlicz functions have been introduced with the lacunary convergence concepts in this paper. Some topological properties of the defined sequence spaces along with the inclusion relations have been investigated.

Lacunary ideal convergence in measure for sequences of fuzzy valued functions

We investigate the concepts of pointwise and uniform I θ -convergence and type of convergence lying between mentioned convergence methods, that is, equi-ideally lacunary convergence of sequences of fuzzy valued functions and acquire several results. We give the lacunary ideal form of Egorov’s theorem for sequences of fuzzy valued measurable functions defined on a finite measure space ( X , M , μ ) . We also introduce the concept of I θ -convergence in measure for sequences of fuzzy valued functions and proved some significant results.

Lacunary difference sequences of complex uncertain
 variables

Using the concept of difference operator on sequence spaces and uncertainty theory, some new class of lacunary convergent difference sequences of complex uncertain variables have been introduced for the lacunary convergence. Some topological properties of the defined sequence spaces along with the inclusion relations have been investigated. <br><br>Користуючись поняттям різницевого оператора на просторі послідовностей і теорією невизначеності, ми досліджуємо клас лакунарно збіжних різницевих послідовностей комплексних невизначених змінних. Розглядаються топологічні властивості введених просторів послідовностей, а також їхні вкладення.

On mathcal{I}_{{theta}_{2}}-convergence in fuzzy normed spaces

In this study, first, lacunary convergence of double sequences is introduced in fuzzy normed spaces, and basic definitions and theorems about lacunary convergence for double sequences are given in fuzzy normed spaces. Then, we introduce the concept of lacunary ideal convergence of double sequences in fuzzy normed spaces, and the relation between lacunary convergence and lacunary ideal convergence is investigated for double sequences in fuzzy normed spaces. Finally, in fuzzy normed spaces, we give the concept of limit point and cluster point for double sequences, and the theorems related to these concepts are given.

$\mathcal{I}$-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.

Subseries convergence and localization properties in sequence spaces supported by ideals in

We investigate various Localization Properties of ideals in relative to sequence spaces supported by them, particularly the Localization Property for Series. The results obtained enable us to prove the existence of a class of sequence spaces X in which every zero-density convergent series is subseries convergent (i.e., X has the Zero Density Convergence Property), but some lacunary convergent series are not (i.e., X fails the Lacunary Convergence Property).

On lacunary p-summable convergence of weight g for fuzzy numbers via ideal

On lacunary p-summable convergence of weight g for fuzzy numbers via ideal

New Definitions about A I -Statistical Convergence with Respect to a Sequence of Modulus Functions and Lacunary Sequences

In this paper, using an infinite matrix of complex numbers, a modulus function and a lacunary sequence, we generalize the concept of I -statistical convergence, which is a recently introduced summability method. The names of our new methods are A I -lacunary statistical convergence and strongly A I -lacunary convergence with respect to a sequence of modulus functions. These spaces are denoted by S θ A I , F and N θ A I , F , respectively. We give some inclusion relations between S A I , F , S θ A I , F and N θ A I , F . We also investigate Cesáro summability for A I and we obtain some basic results between A I -Cesáro summability, strongly A I -Cesáro summability and the spaces mentioned above.

Quasi-Almost Lacunary Statistical Convergence of Sequences of Sets

In this study, we defined concepts of Wijsman quasi-almost lacunary convergence, Wijsman quasi-strongly almost lacunary convergence and Wijsman quasi q-strongly almost lacunary convergence. Also we give the concept of Wijsman quasi-almost lacunary statistically convergence. Then, we study relationships among these concepts. Furthermore, we investigate relationship between these concepts and some convergences types given earlier for sequences of sets, too.

Lacunary I_2-Invariant Convergence and Some Properties

In this paper, the concept of lacunary invariant uniform density of any subset $A$ of the set $\mathbb{N}\times\mathbb{N}$ is defined. Associate with this, the concept of lacunary $\mathcal{I}_2$-invariant convergence for double sequences is given. Also, we examine relationships between this new type convergence concept and the concepts of lacunary invariant convergence and $p$-strongly lacunary invariant convergence of double sequences. Finally, introducing lacunary $\mathcal{I}_2^*$-invariant convergence concept and lacunary $\mathcal{I}_2$-invariant Cauchy concepts, we give the relationships among these concepts and relationships with lacunary $\mathcal{I}_2$-invariant convergence concept.

On Wijsman ℐ2-Lacunary Statistical Convergence for Double Set Sequences

AbstractThe aim of present work is to present some inclusion relations between the concepts of Wijsman ℐ2–lacunary statistical convergence and Wijsman strongly ℐ2–lacunary convergence for double sequences of sets. Also we study the concepts of Wijsman ℐ2–statistical convergence, Wijsman ℐ2– lacunary statistical convergence double sequences of sets and investigate the relationship among them.

Lacunary statistical convergence of double sequences of sets

In this paper, we study the concepts of Wijsman statistical convergence, Wijsman lacunary statistical convergence, Wijsman lacunary convergence and Wijsman strongly lacunary convergence double sequences of sets and investigate the relationship among them.