Almost A-statistical convergence and approximation theorems

In this paper, we define almost A-statistical convergence via almost regular matrices, which extend the notion of regular matrices, and find its relationship with almost A-summability. Then we study its use in a Korovkin-type approximation theorem. We also construct an example such that our new result works but its classical and statistical versions do not work and a figure will be presented to support our result. Finally, we compute the corresponding rate of almost A-statistical convergence of positive linear operators in two different ways, we have newly defined.