Strong law of large numbers for weighted sums of $m$-widely acceptable random variables under sub-linear expectation space

In this article, using the Fuk-Nagaev type inequality, we studied general strong law of large numbers for weighted sums of $m$-widely acceptable ( $m$-WA, for short) random variables under sublinear expectation space with the integral condition

$$\hat{\mathbb{E}}\left(f^{-}\left(\left|X\right|\right)\right)\le {\mathrm{C}}_{\mathbb{V}}\left(f^{-}\left(\left|X\right|\right)\right)<\mathrm{\infty }$$

and $Choquet$ integrals existence, respectively, where

$$f\left(x\right)=x^{1/\beta }L\left(x\right)$$

for $\beta >1$, $L\left(x\right)>0$ $\left(x>0\right)$ was a monotonic nondecreasing slowly varying function, and $f^{-}\left(x\right)$ was the inverse function of $f\left(x\right)$. One of the results included the Kolmogorov-type strong law of large numbers and the partial Marcinkiewicz-type strong law of large numbers for $m$-WA random variables under sublinear expectation space. Besides, we obtained almost surely convergence for weighted sums of $m$-WA random variables under sublinear expectation space. These results improved the corresponding results of Ma and Wu under sublinear expectation space.