We present a new algorithm for Tukey (halfspace) depth level sets and its implementation. Given d-dimensional data set for any d ≥ 2, the algorithm is based on representation of level sets as intersections of balls in R d , and can be easily adapted to related depths (Type D, Zuo and Serfling (Ann. Stat. 28 (2000), 461–482)). The algorithm complexity is… (More)
The Barnes' G-function G(x) = 1/Γ2, satisfies the functional equation log G(x + 1) − log G(x) = log Γ(x). We complement W. Krull's work in Bemerkungen zur Differenzengleichung g(x + 1) − g(x) = ϕ(x), Math. Nachrichten 1 (1948), 365-376 with additional results that yield a different characterization of the function G, new expansions and sharp bounds for G on… (More)
We prove the existence of a solution to the generalized vector equilibrium problem with bounds. We show that several known theorems from the literature can be considered as particular cases of our results, and we provide examples of applications related to best approximations in normed spaces and variational inequalities.