On uniform statistical convergence (Q6084457)

Uniform statistical convergence is well studied and many concepts of statistical convergence have been introduced in the setting of uniform statistical convergence. In the present paper, by using one of these concepts, indeed by using uniform statistical limit superior, the authors obtain two core results for bounded real sequences. They also give a characterization of uniform statistical convergence with the use of inverse Fourier transformation in a similar way which has been used by Schoenberg. They obtain some factorization results for the space of uniformly statistically convergent sequences. As an application of these results, a Korovkin type theorem is provided.