Shape Preserving Properties for q-Bernstein-Stancu Operators
We investigate shape preserving for q-Bernstein-Stancu polynomials Bnq,α(f;x) introduced by Nowak in 2009. When α=0, Bnq,α(f;x) reduces to the well-known q-Bernstein polynomials introduced by Phillips in 1997; when q=1, Bnq,α(f;x) reduces to Bernstein-Stancu polynomials introduced by Stancu in 1968;...
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2014/603694 |
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| author | Yali Wang Yinying Zhou |
| author_facet | Yali Wang Yinying Zhou |
| author_sort | Yali Wang |
| collection | DOAJ |
| description | We investigate shape preserving for q-Bernstein-Stancu polynomials
Bnq,α(f;x) introduced by Nowak in 2009. When α=0, Bnq,α(f;x) reduces to the well-known
q-Bernstein polynomials introduced by Phillips in 1997; when q=1, Bnq,α(f;x) reduces to
Bernstein-Stancu polynomials introduced by Stancu in 1968; when q=1, α=0, we obtain classical Bernstein polynomials. We prove that basic Bnq,α(f;x) basis is a normalized
totally positive basis on [0,1] and q-Bernstein-Stancu operators are variation-diminishing, monotonicity preserving and convexity preserving on [0,1]. |
| format | Article |
| id | doaj-art-535da843ed5b46c0ac5a5da5f9b43bea |
| institution | Kabale University |
| issn | 2314-4629 2314-4785 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-535da843ed5b46c0ac5a5da5f9b43bea2025-08-20T03:36:42ZengWileyJournal of Mathematics2314-46292314-47852014-01-01201410.1155/2014/603694603694Shape Preserving Properties for q-Bernstein-Stancu OperatorsYali Wang0Yinying Zhou1School of Mathematics and Information Science, Langfang Teachers College, Langfang, Hebei 065000, ChinaSchool of Mathematics and Information Science, Langfang Teachers College, Langfang, Hebei 065000, ChinaWe investigate shape preserving for q-Bernstein-Stancu polynomials Bnq,α(f;x) introduced by Nowak in 2009. When α=0, Bnq,α(f;x) reduces to the well-known q-Bernstein polynomials introduced by Phillips in 1997; when q=1, Bnq,α(f;x) reduces to Bernstein-Stancu polynomials introduced by Stancu in 1968; when q=1, α=0, we obtain classical Bernstein polynomials. We prove that basic Bnq,α(f;x) basis is a normalized totally positive basis on [0,1] and q-Bernstein-Stancu operators are variation-diminishing, monotonicity preserving and convexity preserving on [0,1].http://dx.doi.org/10.1155/2014/603694 |
| spellingShingle | Yali Wang Yinying Zhou Shape Preserving Properties for q-Bernstein-Stancu Operators Journal of Mathematics |
| title | Shape Preserving Properties for q-Bernstein-Stancu Operators |
| title_full | Shape Preserving Properties for q-Bernstein-Stancu Operators |
| title_fullStr | Shape Preserving Properties for q-Bernstein-Stancu Operators |
| title_full_unstemmed | Shape Preserving Properties for q-Bernstein-Stancu Operators |
| title_short | Shape Preserving Properties for q-Bernstein-Stancu Operators |
| title_sort | shape preserving properties for q bernstein stancu operators |
| url | http://dx.doi.org/10.1155/2014/603694 |
| work_keys_str_mv | AT yaliwang shapepreservingpropertiesforqbernsteinstancuoperators AT yinyingzhou shapepreservingpropertiesforqbernsteinstancuoperators |