Statistical summability and approximation by de la Vallée-Poussin mean

AbstractIn this paper we define a new type of summability method via statistical convergence by using the density and (V,λ)-summability. We further apply our new summability method to prove a Korovkin type approximation theorem

A Certain Class of Statistical Deferred Weighted A-summability Based on (p; q)-integers and Associated Approximation Theorems

Statistical summability has recently enhanced researchers’ substantial awareness since it is more broad than the traditional (ordinary) convergence. The basic concept of statistical weighted A- summability was introduced by Mohiuddine (2016). In this investigation, we introduce the (presumably new) concept of statistical deferred weighted A-summability and deferred weighted A- statistical convergence with respect to the difference sequence of order r involving (p; q)-integers and establish an inclusion relation between them. Furthermore, based upon the proposed methods, we intend to approximate the rate of convergence and to demonstrate a Korovkin type approximation theorem for functions of two variables defined on a Banach space CB(D). Finally, several illustrative examples are presented in light of our definitions and outcomes established in this paper

Approximation of functions by de la Vall,e-Poussin sums in weighted Orlicz spaces

We investigate problems of estimating the deviation of functions from their de la Vall,e-Poussin sums in weighted Orlicz spaces L (M) (T, omega) in terms of the best approximation E-n (f) M, omega