Deferred Nörlund statistical relative uniform convergence and Korovkin-type approximation theorem

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.

Keywords

• Statistical convergence
• statistical relative uniform convergence
• Nörlund summability
• Korovkin-type approximation theorem
• modulus of continuity

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