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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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
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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| Summary: | 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]. |
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| ISSN: | 2314-4629 2314-4785 |