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$$ {B}_n&#x0005E...
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| Veröffentlicht in: | Mathematical methods in the applied sciences 2024-01, Vol.47 (1), p.5-14 |
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| container_title | Mathematical methods in the applied sciences |
| container_volume | 47 |
| creator | Acu, Ana‐Maria Mutlu, Gökhan Çekim, Bayram Yazıcı, Serdal |
| description | We introduce a new representation of recently introduced perturbed Bernstein operators
BnM$$ {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 $$. In particular, we prove that perturbed Bernstein operators preserve monotonicity and convexity of functions for certain cases. On the other hand, we demonstrate with some counterexamples that monotonicity and convexity preserving properties fail in other cases. Moreover, we present some weaker results in these cases. |
| doi_str_mv | 10.1002/mma.9636 |
| format | Article |
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BnM$$ {B}_n&amp;amp;amp;#x0005E;M $$ in terms of classical Bernstein operators. Using this new representation, we investigate the shape‐preserving properties of the operator
BnM$$ {B}_n&amp;amp;amp;#x0005E;M $$. In particular, we prove that perturbed Bernstein operators preserve monotonicity and convexity of functions for certain cases. On the other hand, we demonstrate with some counterexamples that monotonicity and convexity preserving properties fail in other cases. Moreover, we present some weaker results in these cases.</description><identifier>ISSN: 0170-4214</identifier><identifier>EISSN: 1099-1476</identifier><identifier>DOI: 10.1002/mma.9636</identifier><language>eng</language><publisher>Freiburg: Wiley Subscription Services, Inc</publisher><subject>Bernstein operators ; computer graphics ; computer‐aided design ; Convexity ; Operators ; Representations ; shape‐preserving properties</subject><ispartof>Mathematical methods in the applied sciences, 2024-01, Vol.47 (1), p.5-14</ispartof><rights>2023 John Wiley & Sons Ltd.</rights><rights>2024 John Wiley & Sons, Ltd.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c2936-f2a8286e6082b38732ea1eaa347e47105c910a56610b121b7a9bbe66defefa7e3</citedby><cites>FETCH-LOGICAL-c2936-f2a8286e6082b38732ea1eaa347e47105c910a56610b121b7a9bbe66defefa7e3</cites><orcidid>0000-0003-1192-2281 ; 0000-0002-0674-2908 ; 0000-0002-5363-2453</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://onlinelibrary.wiley.com/doi/pdf/10.1002%2Fmma.9636$$EPDF$$P50$$Gwiley$$H</linktopdf><linktohtml>$$Uhttps://onlinelibrary.wiley.com/doi/full/10.1002%2Fmma.9636$$EHTML$$P50$$Gwiley$$H</linktohtml><link.rule.ids>314,776,780,1411,27901,27902,45550,45551</link.rule.ids></links><search><creatorcontrib>Acu, Ana‐Maria</creatorcontrib><creatorcontrib>Mutlu, Gökhan</creatorcontrib><creatorcontrib>Çekim, Bayram</creatorcontrib><creatorcontrib>Yazıcı, Serdal</creatorcontrib><title>A new representation and shape‐preserving properties of perturbed Bernstein operators</title><title>Mathematical methods in the applied sciences</title><description>We introduce a new representation of recently introduced perturbed Bernstein operators
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BnM$$ {B}_n&amp;amp;amp;#x0005E;M $$ in terms of classical Bernstein operators. Using this new representation, we investigate the shape‐preserving properties of the operator
BnM$$ {B}_n&amp;amp;amp;#x0005E;M $$. 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.</abstract><cop>Freiburg</cop><pub>Wiley Subscription Services, Inc</pub><doi>10.1002/mma.9636</doi><tpages>10</tpages><orcidid>https://orcid.org/0000-0003-1192-2281</orcidid><orcidid>https://orcid.org/0000-0002-0674-2908</orcidid><orcidid>https://orcid.org/0000-0002-5363-2453</orcidid></addata></record> |
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| language | eng |
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| source | Wiley Online Library Journals Frontfile Complete |
| subjects | Bernstein operators computer graphics computer‐aided design Convexity Operators Representations shape‐preserving properties |
| title | A new representation and shape‐preserving properties of perturbed Bernstein operators |
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