Compact operators into the spaces of strongly summable and bounded sequences

Malkowsky, Eberhard; Djolović, Ivana

doi:10.1016/j.na.2011.03.019

Cited by 12 publications

(3 citation statements)

References 22 publications

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“…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%

“…Over the years, it turned out that our software is also useful in the visualization of our scientific results. We applied it for the graphical representations of our results, for instance, in topology [2], crystallography [3], paranormed spaces [4], and Hahn spaces [5]. In this paper, we used it for illustrating some results in functional analysis.…”

Section: Introductionmentioning

confidence: 99%

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Modeling Spheres in Some Paranormed Sequence Spaces

2022

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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.

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Section: Definitionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Modeling Spheres in Some Paranormed Sequence Spaces

2022

Self Cite

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“…The basic version of our software is covered in detail in the book [13]. Later, the software was much improved and applied for the visualization in various fields of mathematics, for example in topology [18] and functional analysis [15,16,17,20], but also in other sciences such as physics [12] and crystallography [14,19].…”

Section: Introductionmentioning

confidence: 99%

Intersections of Surfaces of Revolution

Velickovic

2022

FU Math Inform

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In this paper, we deal with surfaces of revolution and their intersections. We start with the surfaces of revolution RS that have their axis along the x3–axis and find intersections with a line, a plane, and then intersection of two such RS. Furthermore, we apply formulas for the intersection with a line to determine the visibility of RS. Later we develop formulas for the intersection of two surfaces of revolution that have their axis along different arbitrary straight lines, and, as a special case, the intersections of two spheres and intersections of general surface of revolution with a sphere and a surface given by an equation. We apply our own software to the graphical representation of all the results we present.

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On Some Results Using Measures of Noncompactness

Malkowsky

Rakočević

2017

Advances in Nonlinear Analysis via the Concept of Measure of Noncompactness

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Compact operators into the spaces of strongly summable and bounded sequences

Cited by 12 publications

References 22 publications

Modeling Spheres in Some Paranormed Sequence Spaces

Modeling Spheres in Some Paranormed Sequence Spaces

Intersections of Surfaces of Revolution

On Some Results Using Measures of Noncompactness

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