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.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callMore From: Communications Faculty Of Science University of Ankara Series A1Mathematics and Statistics
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
