Complete convergence and complete moment convergence for weighted sums of extended negatively dependent random variables under sub-linear expectation

In this paper, we study the complete convergence and complete moment convergence for weighted sums of extended negatively dependent (END) random variables under sub-linear expectations space with the condition of [Formula: see text], further [Formula: see text], [Formula: see text] ([Formula: see text] is a slow varying and monotone nondecreasing function). As an application, the Baum-Katz type result for weighted sums of extended negatively dependent random variables is established under sub-linear expectations space. The results obtained in the article are the extensions of the complete convergence and complete moment convergence under classical linear expectation space.