Exponential inequalities and a strong law of large numbers for END random variables under sub-linear expectations

The focus of our work is to investigate exponential inequalities for extended negatively dependent (END) random variables in sub-linear expectations. Through these exponential inequalities, we were able to establish the strong law of large numbers with convergence rate $O\left(n^{-1/2}{\ln }^{1/2}n\right)$. Our findings in sub-linear expectation spaces have extended the corresponding results previously established in probability space.