On the Image of the Lupas <i>q</I>-analogue of the Bernstein Operators
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Date
2024
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Springernature
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Green Open Access
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Abstract
The Lupas q-analogue, R-n,R-q, is historically the first known q-version of the Bernstein operator. It has been studied extensively in different aspects by a number of authors during the last decades. In this work, the following issues related to the image of the Lupas q-analogue are discussed: A new explicit formula for the moments has been derived, independence of the image R-n,R-q from the parameter q has been examined, the diagonalizability of operator R-n,R-q has been proved, and the fact that R-n,R-q does not preserve modulus of continuity has been established.
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ORCID
Keywords
Lupas q-transform, Moments, Eigenvalues, Modulus of continuity, Linear operators on function spaces (general), modulus of continuity, Eigenvalue problems for linear operators, eigenvalues, moments, Lupaş \(q\)-transform
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Source
Bulletin of the Malaysian Mathematical Sciences Society
Volume
47
Issue
1
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Scopus : 0
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