Abstract
This is a continuation of the paper (Mizuguchi and Saito, Ann Funct Anal 2:22–33, 2011). We consider the Banach space \({X=(\mathbb{R}^2, \|\cdot\|)}\) with a normalized, absolute norm. We treat three geometric constants; the von Neumann–Jordan constant C NJ(X), the modified von Neumann–Jordan constant \({C^{\prime}_{\rm NJ}(X)}\) and the Zbăganu constant C Z (X). We consider the conditions in which these constants coincide with their upper bound.
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Mizuguchi, H., Saito, KS. On the Upper Bound of Some Geometric Constants of Absolute Normalized Norms on \({\mathbb{R}^2}\) . Mediterr. J. Math. 13, 309–322 (2016). https://doi.org/10.1007/s00009-014-0485-z
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DOI: https://doi.org/10.1007/s00009-014-0485-z