Abstract
In this paper, we will introduce a new geometric constant LYJ(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 LYJ(λ,μ,X). Also, this new coefficient is computed for X being concrete space.
Funder
National Natural Science Foundation of China
Subject
General Mathematics,Engineering (miscellaneous),Computer Science (miscellaneous)
Reference31 articles.
1. On some geometric parameters in Banach spaces
2. On two classes of Banach spaces with uniform normal structure
3. On estimates of the generalized Jordan-von Neumann constant of Banach spaces;Yang;J. Inequalities Pure Appl. Math.,2006
4. Von Neumann–Jordan constant and some geometrical constants of Banach spaces;Kato,1998
5. On James and Jordan–von Neumann constants and the normal structure coefficient of Banach spaces