A Korovkin Type Approximation Theorem and Its Applications
نویسندگان
چکیده
منابع مشابه
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.
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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...
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* 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...
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The well-known result of Korovkin [4] states that for a sequence of positive linear operators [Kn]n 1 , such that Kn f converges uniformly to f in the particular cases f (t)=1, f (t)=t, and f (t)=t, then it also converges for every continuous real function f. The set [1, t, t] is called a Korovkin set. This result was a starting point for the development of a related theory. Since then many pap...
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ژورنال
عنوان ژورنال: Abstract and Applied Analysis
سال: 2014
ISSN: 1085-3375,1687-0409
DOI: 10.1155/2014/859696