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Volume 10
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10.3390/math10060917
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Article

Modeling Spheres in Some Paranormed Sequence Spaces

by
Vesna I. Veličković
1,
Eberhard Malkowsky
2,* and
Edin Dolićanin
3
1
Department of Computer Science, Faculty of Sciences and Mathematics, University of Niš, 18000 Niš, Serbia
2
Department of Mathematics, State University of Novi Pazar, 36300 Novi Pazar, Serbia
3
Department of Technical Sciences, State University of Novi Pazar, 36300 Novi Pazar, Serbia
*
Author to whom correspondence should be addressed.
Mathematics 2022, 10(6), 917; https://doi.org/10.3390/math10060917
Submission received: 11 February 2022 / Revised: 5 March 2022 / Accepted: 10 March 2022 / Published: 13 March 2022
(This article belongs to the Special Issue Modern Geometric Modeling: Theory and Applications II)
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Abstract

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.
Keywords: modeling spheres; shapes of spheres; paranormed sequence spaces; Hahn space; visibility and silhouette modeling spheres; shapes of spheres; paranormed sequence spaces; Hahn space; visibility and silhouette

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MDPI and ACS Style

Veličković, V.I.; Malkowsky, E.; Dolićanin, E. Modeling Spheres in Some Paranormed Sequence Spaces. Mathematics 2022, 10, 917. https://doi.org/10.3390/math10060917

AMA Style

Veličković VI, Malkowsky E, Dolićanin E. Modeling Spheres in Some Paranormed Sequence Spaces. Mathematics. 2022; 10(6):917. https://doi.org/10.3390/math10060917

Chicago/Turabian Style

Veličković, Vesna I., Eberhard Malkowsky, and Edin Dolićanin. 2022. "Modeling Spheres in Some Paranormed Sequence Spaces" Mathematics 10, no. 6: 917. https://doi.org/10.3390/math10060917

APA Style

Veličković, V. I., Malkowsky, E., & Dolićanin, E. (2022). Modeling Spheres in Some Paranormed Sequence Spaces. Mathematics, 10(6), 917. https://doi.org/10.3390/math10060917

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