Abstract
In this paper, we define the concept of statistical relative uniform convergence of the deferred Nörlund mean and we prove a general Korovkin-type approximation theorem by using this convergence method. As an application, we use classical Bernstein polynomials for defining an operator that satisfies our new approximation theorem but does not satisfy the theorem given before. Additionally, we estimate the rate of convergence of approximating positive linear operators by means of the modulus of continuity.
Highlights
Introduction and PreliminariesThe notion of statistical convergence for the sequences of real numbers was introduced by Steinhaus [17] and Fast [11] independently in the same year
We de...ne the concept of statistical relative uniform convergence of the deferred Nörlund mean and we prove a general Korovkintype approximation theorem by using this convergence method
The concept of statistical convergence in approximation theory has been used by Gadjiev and Orhan [12] to prove Korovkin-type approximation theorem
Summary
Introduction and PreliminariesThe notion of statistical convergence for the sequences of real numbers was introduced by Steinhaus [17] and Fast [11] independently in the same year. Statistical convergence, statistical relative uniform convergence, Nörlund summability, Korovkin-type approximation theorem, modulus of continuity.
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