Modulus of convexity, the coefficient \(R(1,X)\), and normal structure in Banach spaces (Q938392)

Summary: Let \(\delta_{X}(\varepsilon )\) and \(R(1,X)\) be the modulus of convexity and the Domínguez--Benavides coefficient, respectively. According to these two geometric parameters, we obtain a sufficient condition for normal structure, that is, a Banach space \(X\) has normal structure if \(2\delta_{X}(1+\varepsilon )>\max\{(R(1,x)-1)\varepsilon,1-(1-\varepsilon /R(1,X)-1)\}\) for some \(\varepsilon\in[0,1]\) which generalizes the known result by Gao and Prus.