On a new geometric constant related to the modulus of smoothness of a Banach space |
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| Authors: | Yasuji Takahashi Mikio Kato |
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| Affiliation: | 1. Department of System Engineering, Okayama Prefectural University, Soja, 719-1197, Japan
2. Department of Mathematics, Faculty of Engineering, Shinshu University, Nagano, 380-8553, Japan
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| Abstract: | We shall introduce a new geometric constant A(X) of a Banach space X, which is closely related to the modulus of smoothness ρ X (τ), and investigate it in relation with the constant A 2(X) by Baronti et al., the von Neumann-Jordan constant C NJ (X) and the James constant J(X). A sequence of recent results on these constants as well as some other geometric constants will be strengthened and improved. |
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| Keywords: | Constant A（X） von Neumann-Jordan constant James constant modulus of smoothness modulus of convexity uniform non-squareness |
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