On paranorm BV<sub>σ</sub> I-convergent double sequence spaces defined by an Orlicz function

Khan, Vakeel A.; Fatima, Hira; Abdullah, Sameera A. A.; Alshlool, Kamal M. A. S.

doi:10.1515/anly-2017-0004

Cited by 4 publications

(3 citation statements)

References 14 publications

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“…Definition 1. ( [3]) Let 2ω = {x = (x nm ) : x nm ∈ R or C} of all real and complex double sequences, where R and C denote the real number set and complex number set, respectively.…”

Section: Introductionmentioning

confidence: 99%

A Generalization of the Strongly Cesaro Ideal Convergence Through Double Sequence Spaces

Granados¹

2021

Int. J. of Appl. Math.

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“…Definition 1. ( [3]) Let 2ω = {x = (x nm ) : x nm ∈ R or C} of all real and complex double sequences, where R and C denote the real number set and complex number set, respectively.…”

Section: Introductionmentioning

confidence: 99%

A Generalization of the Strongly Cesaro Ideal Convergence Through Double Sequence Spaces

Granados¹

2021

Int. J. of Appl. Math.

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“…After that, the notion of ideal convergence (I-convergence) was introduced and studied by Kostyrko et al (2000Kostyrko et al ( , 2005. Later on, it was studied by Šalát et al (2004, 2005), Hazarika (2009, 2011), Khan et al (2014Khan et al ( , 2015Khan et al ( , 2017, Demirci (2001), Gürdal and Sahiner (2008), Nabiev et al (2007), Sahiner et al (2007Sahiner et al ( , 2011, and the references therein. Definition 1.1: Let and be two normed linear spaces.…”

Section: Introductionmentioning

confidence: 99%

On paranorm I-convergent double sequence spaces defined by a compact operator

al.¹

2019

Int. j. adv. appl. sci.

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In this paper, we extend the concept of ideal convergence of sequences in metric spaces. Recently, the concept of ideal convergent double sequence spaces defined by a compact operator. Motivated by this, we introduce some ideal convergent double sequence spaces with the help of compact operator T on the real space ℝ and a bounded double sequence = ( ) of positive real numbers. We examine some basic properties and prove some inclusions relations on these new defined sequence spaces.

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“…The following inequalities will be used throughout the section. Let p ¼ p ij be a double sequence of positive real numbers [19].…”

Section: Introductionmentioning

confidence: 99%

A Study of Bounded Variation Sequence Spaces

Khan¹,

Fatima²,

Ahmad³

2019

Applied Mathematics

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In the theory of classes of sequence, a wonderful application of Hahn-Banach extension theorem gave rise to the concept of Banach limit, i.e., the limit functional defined on c can be extended to the whole space l ∞ and this extended functional is called as the Banach limit. After that, in 1948 Lorentz used this concept of a week limit to introduce a new type of convergence, named as the almost convergence. Later on, Raimi generalized the concept of almost convergence known as σÀ convergence and the sequence space BV σ was introduced and studied by Mursaleen. The main aim of this chapter is to study some new double sequence spaces of invariant means defined by ideal, modulus function and Orlicz function. Furthermore, we also study several properties relevant to topological structures and inclusion relations between these spaces.

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On paranorm BV_σ I-convergent double sequence spaces defined by an Orlicz function

Abstract: The space

Cited by 4 publications

References 14 publications

A Generalization of the Strongly Cesaro Ideal Convergence Through Double Sequence Spaces

A Generalization of the Strongly Cesaro Ideal Convergence Through Double Sequence Spaces

On paranorm I-convergent double sequence spaces defined by a compact operator

A Study of Bounded Variation Sequence Spaces

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On paranorm BVσ I-convergent double sequence spaces defined by an Orlicz function

Abstract: The space

Cited by 4 publications

References 14 publications

A Generalization of the Strongly Cesaro Ideal Convergence Through Double Sequence Spaces

A Generalization of the Strongly Cesaro Ideal Convergence Through Double Sequence Spaces

On paranorm I-convergent double sequence spaces defined by a compact operator

A Study of Bounded Variation Sequence Spaces

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On paranorm BV_σ I-convergent double sequence spaces defined by an Orlicz function