6533b861fe1ef96bd12c436f

RESEARCH PRODUCT

Modified Operators Interpolating at Endpoints

Ana Maria AcuRekha SrivastavaIoan Raşa

subject

General MathematicsOrder (ring theory)iteratesIterated functionMarkov operatorsComputer Science (miscellaneous)QA1-939Applied mathematicsdifferences of operatorsAffine transformationEngineering (miscellaneous)MathematicsMathematicsVoronovskaja-type results

description

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.

yearjournalcountryeditionlanguage
2021-08-25Mathematics
10.3390/math9172051https://www.mdpi.com/2227-7390/9/17/2051