Approximation of Periodic Functions via Statistical 𝓑-summability and Its Applications to Approximation Theorems

The A-statistical summability is stronger than A-statistical convergence which was introduced by Edely and Mursaleen [7] (see [Edely and Mursaleen, On statistical A-summability, Math. Comput. Model.49, 672–680). In this paper, by using the concept of statistical 𝓑-summability we establish a result on Korovkin-type approximation theorem for periodic functions defined on a Banach space C^∗(𝓡), which is also stronger than its statistical A-summability version. Furthermore, we demonstrate a theorem for the rate of the 𝓑-statistical convergence for same set of functions with the help of the modulus of continuity.