2025/04/02 by Wang, Yuxin, Liu, Qi, Xia, Jinyu +1
#46B20 #46C15 #F.2.23 #FOS: Mathematics #Functional Analysis (math.FA)
paper · doi:10.48550/arxiv.2504.01267
The p-angular distance was first introduced by Maligranda in 2006, while the skew p-angular distance was first introduced by Rooin in 2018. In this paper, we shall introduce a new geometric constant named Maligranda-Rooin constant in Banach spaces to compare p-angular distance and skew p-angular distance. We denote the Maligranda-Rooin constant as M Rp(X). First, the upper and lower bounds for the M Rp(X) constant is given. Next, it's shown that, a normed linear space is an inner space if and only if M Rp(X)=1. Moreover, an equivalent form of this new constant is established. By means of the M Rp(X) constant, we carry out the quantification of the characterization of uniform nonsquareness. Finally, we study the relationship between the M Rp(X) constant, uniform convexity, uniform smooth and normal structure.