... remainder of this paper is organized as follows. In Section 2, we present the main theorems of this paper. In Section 3, the proofs of the maintheorems in this paper are presented.2. Main Theorems In ... convergence theorem for sequence of martingaledifferences. Then, Qiu 14 extended the result of Wang and Yang in 2008. The purpose of this paper is to discuss f urther the strong limit theorems for ... cases of this paper. In addition, the main theorems of this paperextend the main results by Wang and Guo in 2009, Qiu and Yang in 1999, and the result byWang and Yang in 2005, respectively. The...