Affiliation:
1. Department of Mathematics, Sun Yat-sen University , Guangzhou , 510275 , P. R. China
Abstract
Abstract
We shall introduce a new geometric constant
C
Z
(
λ
,
μ
,
X
)
{C}_{Z}\left(\lambda ,\mu ,X)
based on a generalization of the parallelogram law, which was proposed by Moslehian and Rassias. First, it is shown that, for a Banach space,
C
Z
(
λ
,
μ
,
X
)
{C}_{Z}\left(\lambda ,\mu ,X)
is equal to 1 if and only if the norm is induced by an inner product. Next, a characterization of uniformly non-square is given, that is,
X
X
has the fixed point property. Also, a sufficient condition which implies weak normal structure is presented. Moreover, a generalized James constant
J
(
λ
,
X
)
J\left(\lambda ,X)
is also introduced. Finally, some basic properties of this new coefficient are presented.
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