Modified Operators Interpolating at Endpoints

Ana Maria Acu, Ioan Raşa and Rekha Srivastava
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Ana Maria Acu: Department of Mathematics and Informatics, Lucian Blaga University of Sibiu, Str. Dr. I. Ratiu, No. 5-7, 550012 Sibiu, Romania
Ioan Raşa: Department of Mathematics, Technical University of Cluj-Napoca, Str. Memorandumului nr. 28, 400114 Cluj-Napoca, Romania
Rekha Srivastava: Department of Mathematics and Statistics, University of Victoria, Victoria, BC V8W 3R4, Canada

Mathematics, 2021, vol. 9, issue 17, 1-13

Abstract: Some classical operators (e.g., Bernstein) preserve the affine functions and consequently interpolate at the endpoints. Other classical operators (e.g., Bernstein–Durrmeyer) have been modified in order to preserve the affine functions. We propose a simpler modification with the effect that the new operators interpolate at endpoints although they do not preserve the affine functions. We investigate the properties of these modified operators and obtain results concerning iterates and their limits, Voronovskaja-type results and estimates of several differences.

Keywords: Markov operators; iterates; Voronovskaja-type results; differences of operators (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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