The skew James type constant in Banach spaces

In the past, Takahashi has introduced the James type constants $\mathcal{J}_{\mathcal{X} ,t}(\tau)$. Building upon this foundation, we introduce an innovative skew James type constant, denoted as $\mathcal{J}_t[\tau,\mathcal{X}]$, which is perceived as a skewed counterpart to the traditional James type constants. We delineate a novel constant, and proceed to ascertain its equivalent representations along with certain attributes within the context of Banach spaces, and then an investigation into the interrelation between the skewness parameter and the modulus of convexity is conducted, after that we define another new constant $\mathcal{G}_t(\mathcal{X})$, and some conclusions were drawn.