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Volume 13
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Article

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

by
Asif Ahmad
,
Qi Liu
* and
Yongjin Li
School of Mathematics, Sun Yat-sen University, Guangzhou 510275, China
*
Author to whom correspondence should be addressed.
Symmetry 2021, 13(7), 1294; https://doi.org/10.3390/sym13071294
Submission received: 4 July 2021 / Revised: 17 July 2021 / Accepted: 18 July 2021 / Published: 19 July 2021
(This article belongs to the Special Issue Functional Equations and Inequalities 2021)
Versions Notes

Abstract

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.
Keywords: Banach spaces; geometric constants; geometry of normed spaces; normal structure Banach spaces; geometric constants; geometry of normed spaces; normal structure

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MDPI and ACS Style

Ahmad, A.; Liu, Q.; Li, Y. Geometric Constants in Banach Spaces Related to the Inscribed Quadrilateral of Unit Balls. Symmetry 2021, 13, 1294. https://doi.org/10.3390/sym13071294

AMA Style

Ahmad A, Liu Q, Li Y. Geometric Constants in Banach Spaces Related to the Inscribed Quadrilateral of Unit Balls. Symmetry. 2021; 13(7):1294. https://doi.org/10.3390/sym13071294

Chicago/Turabian Style

Ahmad, Asif, Qi Liu, and Yongjin Li. 2021. "Geometric Constants in Banach Spaces Related to the Inscribed Quadrilateral of Unit Balls" Symmetry 13, no. 7: 1294. https://doi.org/10.3390/sym13071294

APA Style

Ahmad, A., Liu, Q., & Li, Y. (2021). Geometric Constants in Banach Spaces Related to the Inscribed Quadrilateral of Unit Balls. Symmetry, 13(7), 1294. https://doi.org/10.3390/sym13071294

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