let  be a sequence of arbitrary random variables with  and , for every  and  be an array of real numbers. we will obtain two maximal inequalities for partial sums and weighted sums of random variables and also, we will prove complete convergence for weighted sums , under some conditions on  and sequence .

Let  be a sequence of arbitrary random variables with  and , for every  and  be an array of real numbers. We will obtain two maximal inequalities for partial sums and weighted sums of random variables and also, we will prove complete convergence for weighted sums , under some conditions on  and sequence .

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...