A Korovkin type theorem on weak convergence

Matrix Summability and Korovkin Type Approximation Theorem on Modular Spaces

In this paper, using a matrix summability method we obtain a Korovkin type approximation theorem for a sequence of positive linear operators defined on a modular space.

Variations on a Theorem of Korovkin

A - Statistical extension of the Korovkin type approximation theorem

Let A = (a jn) be an infinite summability matrix. For a given sequence x := (xn), the A-transform of x, denoted by Ax := ((Ax) j), is given by (Ax) j = ∑n=1 a jnxn provided the series converges for each j ∈ N, the set of all natural numbers. We say that A is regular if limAx = L whenever limx = L [4]. Assume that A is a non-negative regular summability matrix. Then x = (xn) is said to be A-stat...

Korovkin Type Theorem for Functions of Two Variables via Lacunary Equistatistical Convergence

Aktuğlu and Gezer [1] introduced the concepts of lacunary equistatistical convergence, lacunary statistical pointwise convergence and lacunary statistical uniform convergence for sequences of functions. Recently, Kaya and Gönül [11] proved some analogs of the Korovkin approximation theorem via lacunary equistatistical convergence by using test functions 1, x 1+x , y 1+y , ( x 1+x )2+( y 1+y )2....

Weighted statistical convergence and its application to Korovkin type approximation theorem

In this paper, we introduce the concepts of weighted ideal statistical convergence or SN (I)-convergence and I − (N, pn)-summability. We also establish the relations between our new methods. Further, we determine a Korovkin type approximation theorem through I − (N, pn)-summability. −−−−−−−−−−−−−−−−−−−−−−−−−−−−