I-lacunary statistical convergence of sequences of sets

Facta Universitatis, Series: Mathematics and Informatics, 2023

In this article, we introduce the concepts of Wijsman deferred statistical convergence and Wijsman strong deferred Cesaro summability for double sequences of sets. Additionally, some properties and based results have been established under a few restrictions.

Mathematical Sciences and Applications E-Notes

This paper presents, for sequences of sets, generalize the concepts of Wijsman asymptotically strongly I-lacunary equivalence and Wijsman asymptotically strongly I-Cesàro equivalence by using p = (p k) which is the sequence of positive real numbers where I is an ideal of the subset of the set N of natural numbers.

FOURTH INTERNATIONAL CONFERENCE OF MATHEMATICAL SCIENCES (ICMS 2020)

The main purpose of this paper is to introduce the concepts of Wijsman deferred statistical convergence of order α and Wijsman strong deferred Cesàro convergence of order α for sequences of sets.

Annals of the University of Craiova, Mathematics and Computer Science Series

In this paper, we introduce and investigate the notion of lacunary statistical convergence of sequences in gradual normed linear spaces. We study some of its basic properties and some inclusion relations. In the end, we introduce the notion of lacunary statistical Cauchy sequences and prove that it is equivalent to the notion of lacunary statistical convergence.

In this paper we introduce the concepts of Wijsman (f, I) −lacunary statistical convergence of order α and Wijsman strongly (f, I) −lacunary statistical convergence of order α, and investigated between their relationship.

European Journal of Pure and Applied Mathematics, 2013

The concept of Wijsman statistical convergence was defined by Nuray and Rhoades [9]. In this paper we define statistically almost - convergence for sequences for sets in sense of Wijsman and study some properties of this concept.

International Journal of Analysis and Applications

In this paper, we defined concept of Wijsman I-Cesàro summability for sequences of sets and investigate the relationships between the concepts of Wijsman strongly I-Cesàro summability and Wijsman statistical I− Cesàro summability by using the concept of a triple sequence spaces.

Proyecciones (Antofagasta), 2021

In this paper we investigate the notion of I-statistical ϕ-convergence and introduce IS-ϕ limit points and IS-ϕ cluster points of real number sequence and also studied some of its basic properties.

2005

A lacunary sequence is an increasing integer sequence θ = (kr) such that k0 =0, kr −kr−1 → ∞ as r → ∞. A sequence x is called S θ (∆ m)− convergent to L provided that for each ε > 0, limr(kr − kr−1) −1 {the number of kr−1 < k ≤ kr : |∆ m x k −L| ≥ ε} = 0, where ∆ m x k = ∆ m−1 x k − ∆ m−1 x k+1. The purpose of this paper is to introduce the concept of ∆ m − lacunary statistical convergence and ∆ m-lacunary strongly convergence and examine some properties of these sequence spaces. We establish some connections between ∆ m-lacunary strongly convergence and ∆ m-lacunary statistical convergence. It is shown that if a sequence is ∆ m-lacunary strongly convergent then it is ∆ m-lacunary statistically convergent. We also show that the space S θ (∆ m) may be represented as a [f, p, θ](∆ m) space.

IOSR Journals , 2019

In this paper, we shall introduce the extension of recently introduced concepts of Wijsman I−lacunary statistical convergence of order 𝛼 and Wijsman strongly 𝐼 −lacunary statistical convergenceof order 𝛼to double sequences.

THIRD INTERNATIONAL CONFERENCE OF MATHEMATICAL SCIENCES (ICMS 2019)

In this paper, the definitions of lacunary strong A−convergence of order (α, β) with respect to a modulus and lacunary A−statistical convergence of order (α, β) are given. We study some connections between lacunary strong A−convergence of order (α, β) with respect to a modulus and lacunary A−statistical convergence of order (α, β).

2018

Let w be the set of all real or complex sequences and l∞, c and c0 respectively, be the Banach spaces of bounded, convergent and null sequences x = (xk), normed by ‖x‖ = sup k |xk|, where k ∈ N. Let X and Y be two sequence spaces and A = (aik) be an infinite matrix of real or complex numbers aik, where i, k ∈ N. Then we say that A defines a matrix mapping from X into Y if for every sequence x = (xi) ∈ X, the sequence Ax = {Ai(x)}, the A-transform of x, is in Y , where

THIRD INTERNATIONAL CONFERENCE OF MATHEMATICAL SCIENCES (ICMS 2019)

In this study, using a lacunary sequence we introduce the concepts of lacunary d−statistically convergent sequences and lacunary d−statistically bounded sequences in general metric spaces.

Journal of Inequalities and Applications, 2017

In this paper, the idea of lacunary I λ-statistical convergent sequence spaces is discussed which is defined by a Musielak-Orlicz function. We study relations between lacunary I λ-statistical convergence with lacunary I λ-summable sequences. Moreover, we study the I λ-lacunary statistical convergence in probabilistic normed space and discuss some topological properties.

Arab Journal of Mathematical Sciences, 2014

In this paper, we define some new sequence spaces of lacunary convergent sequences derived by No¨rlund-type (Riesz) mean, which shall be denoted by j N ; p r ; h j and ðN ; p r ; hÞ, and investigate some relations between the sequence space j N ; p r ; h j with the spaces OEw h OE and j N ; p n j. Further, we define a new concept, named weighted lacunary statistical convergence and examine some connections between this notion with the concept of lacunary statistical convergence and weighted statistical convergence. Also, some topological properties of these new sequence spaces are investigated.