On a New Geometric Constant Related to the Euler-Lagrange Type Identity in Banach Spaces

Qi Liu and Yongjin Li
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Qi Liu: School of Mathematics, Sun Yat-Sen University, Guangzhou 510275, China
Yongjin Li: School of Mathematics, Sun Yat-Sen University, Guangzhou 510275, China

Mathematics, 2021, vol. 9, issue 2, 1-12

Abstract: In this paper, we will introduce a new geometric constant L YJ ( λ , μ , X ) based on an equivalent characterization of inner product space, which was proposed by Moslehian and Rassias. We first discuss some equivalent forms of the proposed constant. Next, a characterization of uniformly non-square is given. Moreover, some sufficient conditions which imply weak normal structure are presented. Finally, we obtain some relationship between the other well-known geometric constants and L YJ ( λ , μ , X ) . Also, this new coefficient is computed for X being concrete space.

Keywords: uniformly non-square Banach space; von Neumann–Jordan constant; Euler-Lagrange type identity (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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