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Modeling Spheres in Some Paranormed Sequence Spaces

Author

Listed:
  • 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)

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.

Suggested Citation

  • Vesna I. Veličković & Eberhard Malkowsky & Edin Dolićanin, 2022. "Modeling Spheres in Some Paranormed Sequence Spaces," Mathematics, MDPI, vol. 10(6), pages 1-15, March.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:6:p:917-:d:770198
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