Convergence in $$\boldsymbol{r}$$-Mean of Arrays of Rowwise Widely Orthant Dependent Random Variables

In this paper, we refine the mean convergence result of order $$r\ (1\leq r<2)$$ for arrays of rowwise widely orthant dependent random variables. Specifically, we address an open problem posed by Thành (RACSAM 118(1): Paper No. 40, 2024), who suggested that his method could improve the result of Wu et al. (Stochastics 91 (6), 926–944 (2019)) by relaxing its restrictive assumptions. By applying Thành’s weaker criterion, we enhance the mean convergence result for arrays of rowwise widely orthant dependent random variables with general norming constants, thereby providing a significant refinement of Wu et al.’s findings.