A new representation and shape‐preserving properties of perturbed Bernstein operators

We introduce a new representation of recently introduced perturbed Bernstein operators BnM$$ {B}_n^M $$ in terms of classical Bernstein operators. Using this new representation, we investigate the shape‐preserving properties of the operator BnM$$ {B}_n&#x0005E...

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Bibliographic Details
Published in:Mathematical methods in the applied sciences 2024-01, Vol.47 (1), p.5-14
Main Authors: Acu, Ana‐Maria, Mutlu, Gökhan, Çekim, Bayram, Yazıcı, Serdal
Format: Article
Language:English
Subjects:
Bernstein operators
computer graphics
computer‐aided design
Convexity
Operators
Representations
shape‐preserving properties
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Summary:We introduce a new representation of recently introduced perturbed Bernstein operators BnM$$ {B}_n^M $$ in terms of classical Bernstein operators. Using this new representation, we investigate the shape‐preserving properties of the operator BnM$$ {B}_n^M $$. In particular, we prove that perturbed Bernstein operators preserve monotonicity and convexity of functions for certain cases. On the other hand, we demonstrate with some counterexamples that monotonicity and convexity preserving properties fail in other cases. Moreover, we present some weaker results in these cases.
ISSN:0170-4214
1099-1476
DOI:10.1002/mma.9636