Paper Title:

Some Moduli and Inequalities Related to Birkhoff Orthogonality in Banach Spaces

Author(s):

Dandan Du and Yongjin Li

Department of Mathematics,
Sun Yat-sen University,
Guangzhou, 510275,
P.R. China.
E-mail: dudd5@mail2.sysu.edu.cn

 
Department of Mathematics,
Sun Yat-sen University,
Guangzhou, 510275,
P.R. China.
E-mail: stslyj@mail.sysu.edu.cn 

Abstract:

In this paper, we shall consider two new constants δ_B(X) and ρ_B(X), which are the modulus of convexity and the modulus of smoothness related to Birkhoff orthogonality, respectively. The connections between these two constants and other well-known constants are established by some equalities and inequalities. Meanwhile, we obtain two characterizations of Hilbert spaces in terms of these two constants, study the relationships between the constants δ_B(X), ρ_B(X) and the fixed point property for nonexpansive mappings. Furthermore, we also give a characterization of the Radon plane with affine regular hexagonal unit sphere.

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