Research Article

Arithmetic for closed balls

Published in: Quaestiones Mathematicae
Volume 45 , issue 9 , 2022 , pages: 1459–1471

DOI: 10.2989/16073606.2021.1949402

Author(s): P.D. Beites , Portugal , A.P. Nicolás , España , José Vitória , Portugal

Keywords: 15A69 , 15A72 , 15A99 , 08A40 , 15A66 , 17A75 , 15A69 , 15A72 , 15A99 , 08A40 , 15A66 , 17A75

Abstract

Inspired by circular complex interval arithmetic, an arithmetic for closed balls in ℝ ⁿ is pursued. In this sense, the properties of certain operations on closed balls in ℝ ⁿ , some of which related either to the Hadamard product of vectors or to the 2-fold vector cross product when n ∈ {3,7}, are studied. In particular, known results for operations on closed balls in ℂ, which can be identified with ℝ², are extended to closed balls in ℝ ⁿ .

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