In this article, we investigate a central limit theorem for weighted sum of independent random variables under sublinear expectations. It is turned out that our results are natural extensions of the results obtained by Peng ( 2008 Peng , S. (2008). A New Central Limit Theorem under Sublinear Expectations. arXiv:0803. 2656vl [math.PR]. [Google Scholar] ) and Li and Shi ( 2010 Li , M. , Shi , Y. ( 2010 ). A general central limit theorem under sublinear expectations . Sci. China Ser. A 53 : 1989 – 1994 . [Crossref] [Google Scholar] ).

In this Note, our aim is to obtain the central limit theorem for capacities induced by sublinear expectations.

Impulsive Cohen‐Grossberg neural networks with bounded and unbounded delays (i.e., mixed delays) are investigated. By using the Leray‐Schauder fixed point theorem, differential inequality techniques, and constructing suitable Lyapunov functional, several new sufficient conditions on the existence and global exponential stability of periodic solution for the system are obtained, which improves some of the known results. An example and its numerical simulations are employed to illustrate our feasible results.