Modeling Spheres in Some Paranormed Sequence Spaces

Vesna I. Veličković, Eberhard Malkowsky and Edin Dolićanin
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Vesna I. Veličković: Department of Computer Science, Faculty of Sciences and Mathematics, University of Niš, 18000 Niš, Serbia
Eberhard Malkowsky: Department of Mathematics, State University of Novi Pazar, 36300 Novi Pazar, Serbia
Edin Dolićanin: Department of Technical Sciences, State University of Novi Pazar, 36300 Novi Pazar, Serbia

Mathematics, 2022, vol. 10, issue 6, 1-15

Abstract: We introduce a new sequence space h A ( 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 h A ( p ) reduces to the generalized Hahn space h d . We applied our own software to visualize the shapes of parts of spheres in three-dimensional space endowed with the relative paranorm of h A ( 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.

Keywords: modeling spheres; shapes of spheres; paranormed sequence spaces; Hahn space; visibility and silhouette (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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