Journal of Convex Analysis 33 (2026), No. 1&2, 171--181
Copyright Heldermann Verlag 2026
Lipschitzness of the Width and Diameter Functions of Convex Bodies in Rn
Oleg Mushkarov
Inst. of Mathematics and Informatics, Bulgarian Academy of Sciences, Sofia, Bulgaria
muskarov@math.bas.bg
Nikolai Nikolov
(1) Inst. of Mathematics and Informatics, Bulgarian Academy of Sciences, Sofia, Bulgaria
(2) Faculty of Information Sciences, State University of Library Studies and Information Technologies, Sofia, Bulgaria
nik@math.bas.bg
Pascal J. Thomas
Institut de Mathématiques, UMR5219, Université de Toulouse, Toulouse, France
pascal.thomas@math.univ-toulouse.fr
Lipschitz constants for the width and diameter functions of a convex body in Rn are found in terms of its diameter and thickness (maximum and minimum of both functions). Also, a dual approach to thickness is proposed.
Keywords: Convex body, diameter, width, thickness, Lipschitzness.
MSC: 52A20.
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