The roots of polynomials and the operator $$\Delta _i^3$$ on the Hahn sequence space h

Malkowsky, Eberhard; Milovanović, Gradimir V.; Rakočević, Vladimir; Tuǧ, Orhan

doi:10.1007/s40314-021-01611-6

Cited by 10 publications

(8 citation statements)

References 8 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…It was shown in [15], Proposition 2.1, that if the sequence d is increasing and unbounded, then h d is a BK space with AK. Matrix transformations and bounded and compact operators on the Hahn space have recently been studied in various papers, for instance in [5,[15][16][17][18][19][20][21][22][23]. Spectra on the Hahn space were studied in [16,24,25].…”

Section: Definitionmentioning

confidence: 99%

See 1 more Smart Citation

Modeling Spheres in Some Paranormed Sequence Spaces

2022

Self Cite

View full text Add to dashboard Cite

We introduce a new sequence space hA(p), which is not normable, in general, and show that it is a paranormed space. Here, A and p denote an infinite matrix and a sequence of positive numbers. In the special case, when A is a diagonal matrix with a sequence d of positive terms on its diagonal and p=(1,1,⋯), then hA(p) reduces to the generalized Hahn space hd. We applied our own software to visualize the shapes of parts of spheres in three-dimensional space endowed with the relative paranorm of hA(p), when A is an upper triangle. For this, we developed a parametric representation of these spheres and solved the visibility and contour (silhouette) problems. Finally, we demonstrate the effects of the change of the entries of the upper triangle A and the terms of the sequence p on the shape of the spheres.

show abstract

Section: Definitionmentioning

confidence: 99%

“…Matrix transformations and bounded and compact operators on the Hahn space have recently been studied in various papers, for instance in [5,[15][16][17][18][19][20][21][22][23]. Spectra on the Hahn space were studied in [16,24,25]. A survey of recent results can also be found in [18].…”

Section: Definitionmentioning

confidence: 99%

Modeling Spheres in Some Paranormed Sequence Spaces

2022

Self Cite

View full text Add to dashboard Cite

show abstract

“…e generalized difference matrix Δ 3 i � (δ nk ) of order three was defined by Malkowsky et al [7] as…”

Section: The New Difference Sequence Spacesmentioning

confidence: 99%

The Generalized Difference Operator Δi3 of Order Three and Its Domain in the Sequence Spaces ℓ₁ and bv

Tuǧ

2022

Journal of Mathematics

View full text Add to dashboard Cite

Most recently, the generalized difference operator Δ i 3 of order three was defined and its domain in Hahn sequence space h was calculated. In this paper, the spaces ℓ 1 Δ i 3 and b v Δ i 3 are introduced as the domain of generalized difference operator Δ i 3 of order three in the sequence spaces ℓ 1 and b v . Then, some topological properties of ℓ 1 Δ i 3 and b v Δ i 3 are given, and some inclusion relations are shown. Additionally, algebraic dual, α − , β − , and γ − dual spaces of ℓ 1 Δ i 3 and b v Δ i 3 are computed. In the last section, the classes μ Δ i 3 : λ and λ : μ Δ i 3 of matrix transformations are characterized, where μ = ℓ 1 , b v and λ = c , c 0 , ℓ 1 , ℓ ∞ , b s , c s , b v , h .

show abstract

“…Besides, the authors stated and proved various significant results concerning characterization of matrix transformations between the space h d and classical BK spaces, and characterization of compact operators on the space h d using Hausdorff measure of noncompactness. We refer to [2,10,[13][14][15][16][17][18][19][20][21][22][23] and the survey paper [22] for more studies and results related to Hahn sequence space.…”

Section: Introduction and Basic Notationsmentioning

confidence: 99%

On the New Generalized Hahn Sequence Space $h_{d}^{p}$

Tuǧ

Malkowsky

Hazarika

et al. 2022

Abstract and Applied Analysis

Self Cite

View full text Add to dashboard Cite

In this article, we define the new generalized Hahn sequence space h d p , where d = d k k = 1 ∞ is monotonically increasing sequence with d k ≠ 0 for all k ∈ ℕ , and 1 < p < ∞ . Then, we prove some topological properties and calculate the α − , β − , and γ − duals of h d p . Furthermore, we characterize the new matrix classes h d , λ , where λ = b v , b v p , b v ∞ , b s , c s , , and μ , h d , where μ = b v , b v 0 , b s , c s 0 , c s . In the last section, we prove the necessary and sufficient conditions of the matrix transformations from h d p into λ = ℓ ∞ , c , c 0 , ℓ 1 , h d , b v , b s , c s , and from μ = ℓ 1 , b v 0 , b s , c s 0 into h d p .

show abstract

The roots of polynomials and the operator $$\Delta _i^3$$ on the Hahn sequence space h

Cited by 10 publications

References 8 publications

Modeling Spheres in Some Paranormed Sequence Spaces

Modeling Spheres in Some Paranormed Sequence Spaces

The Generalized Difference Operator Δi3 of Order Three and Its Domain in the Sequence Spaces ℓ₁ and bv

On the New Generalized Hahn Sequence Space $h_{d}^{p}$

Contact Info

Product

Resources

About

The roots of polynomials and the operator $$\Delta _i^3$$ on the Hahn sequence space h

Cited by 10 publications

References 8 publications

Modeling Spheres in Some Paranormed Sequence Spaces

Modeling Spheres in Some Paranormed Sequence Spaces

The Generalized Difference Operator Δi3 of Order Three and Its Domain in the Sequence Spaces ℓ1 and bv

On the New Generalized Hahn Sequence Space h d p

Contact Info

Product

Resources

About

The Generalized Difference Operator Δi3 of Order Three and Its Domain in the Sequence Spaces ℓ₁ and bv

On the New Generalized Hahn Sequence Space $h_{d}^{p}$