A Spline Group – Korovkin Approximation Theorem

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...

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

Korovkin type approximation theorem for functions of two variables through statistical A-summability

* Correspondence: [email protected] Department of Mathematics, Aligarh Muslim University, Aligarh 202002, India Full list of author information is available at the end of the article Abstract In this article, we prove a Korovkin type approximation theorem for a function of two variables by using the notion of statistical A-summability. We also study the rate of statistical A-summability of p...

A-statistical Korovkin-type Approximation Theorem for Functions of Two Variables on an Infinite Interval

In this paper, using the concept of A-statistical convergence for double sequences, we provide a Korovkin-type approximation theorem for positive linear operators on the space of all real-valued uniform continuous functions on [0,∞) × [0,∞) with the property that have a finite limit at the infinity. Then, we display an application which shows that our new result is stronger than its classical v...