Hence complete moment convergence is more general than complete convergence.
Chow [11] first investigated the complete moment convergence, which is more exact than complete convergence.
Chow (1988 [8]) first investigated the complete moment convergence, which is more exact than complete convergence.
random variables with mean zero, Chow [14] first investigated the complete moment convergence, which is more exact than complete convergence.
For more details about the complete convergence result for weighted sums of dependent sequences, one can refer to Wu [24, 25], Wang et al. [26, 27], and so forth.
The complete moment convergence is a more general version of the complete convergence.
The purpose of this paper is extending Theorem A to the complete moment convergence, which is a more general version of the complete convergence.
In addition, the results and conditions of this paper include a slow varying and monotone nondecreasing function, so the theorems are more generic than the traditional complete convergence.
Motivated by the work of Sung [9], the aim of this paper is to obtain the complete convergence under more general moment conditions.
For more results of strong convergence, complete convergence and the applications, one can refer to Hu et al. [25], Rosalsky and Volodin [26], Wang et al. [27], Wu et al. [28], Yang et al. [29], Yang and Hu [30], Wang et al. [31] and so on.
