wUR modulus and normal structure in Banach spaces

Document Type: Original Article



‎Let $X$ be a Banach space‎. ‎In this paper‎, ‎we study the properties of wUR modulus of $X$‎, ‎$\delta_X(\varepsilon‎, ‎f),$ where $0 \le \varepsilon \le 2$ and $f \in S(X^*),$ and the relationship between the values of wUR modulus and reflexivity‎, ‎uniform non-squareness and normal structure respectively‎. ‎Among other results‎, ‎we proved that if $ \delta_X(1‎, ‎f)> 0$ for any $f\in S(X^*),$ then $X$ has weak normal structure‎.