Geometric Constants in Banach Spaces Related to the Inscribed Quadrilateral of Unit Balls

We introduce a new geometric constant Jin(X) based on a generalization of the parallelogram law, which is symmetric and related to the length of the inscribed quadrilateral side of the unit ball. We first investigate some basic properties of this new coefficient. Next, it is shown that, for a Banach...

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Bibliographic Details
Published in:Symmetry (Basel) 2021-07, Vol.13 (7), p.1294
Main Authors: Ahmad, Asif, Liu, Qi, Li, Yongjin
Format: Article
Language:English
Subjects:
Banach spaces
Euclidean space
geometric constants
Geometry
geometry of normed spaces
normal structure
Quadrilaterals
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Summary:We introduce a new geometric constant Jin(X) based on a generalization of the parallelogram law, which is symmetric and related to the length of the inscribed quadrilateral side of the unit ball. We first investigate some basic properties of this new coefficient. Next, it is shown that, for a Banach space, Jin(X) becomes 16 if and only if the norm is induced by an inner product. Moreover, its properties and some relations between other well-known geometric constants are studied. Finally, a sufficient condition which implies normal structure is presented.
ISSN:2073-8994
2073-8994
DOI:10.3390/sym13071294