On the Sets of Convergence for Sequences of the ๐-Bernstein Polynomials with ๐>1
The aim of this paper is to present new results related to the convergence of the sequence of the ๐-Bernstein polynomials {๐ต๐,๐(๐;๐ฅ)} in the case ๐>1, where ๐ is a continuous function on [0,1]. It is shown that the polynomials converge to ๐ uniformly on the time scale ๐๐={๐โ๐}โ๐=0โช{0}, and that...
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| Format: | Article |
| Language: | English |
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Wiley
2012-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2012/185948 |
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| author | Sofiya Ostrovska Ahmet Yaลar รzban |
| author_facet | Sofiya Ostrovska Ahmet Yaลar รzban |
| author_sort | Sofiya Ostrovska |
| collection | DOAJ |
| description | The aim of this paper is to present new results related to the convergence of the sequence of the ๐-Bernstein polynomials {๐ต๐,๐(๐;๐ฅ)} in the case ๐>1, where ๐ is a continuous function on [0,1]. It is shown that the polynomials converge to ๐ uniformly on the time scale ๐๐={๐โ๐}โ๐=0โช{0}, and that this result is sharp in the sense that the sequence {๐ต๐,๐(๐;๐ฅ)}โ๐=1 may be divergent for all ๐ฅโ๐
โงต๐๐. Further, the impossibility of the uniform approximation for the Weierstrass-type functions is established. Throughout the paper, the results are illustrated by numerical examples. |
| format | Article |
| id | doaj-art-503f82594a7e44d0919e5d0e1e37c670 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-503f82594a7e44d0919e5d0e1e37c6702025-02-03T01:04:51ZengWileyAbstract and Applied Analysis1085-33751687-04092012-01-01201210.1155/2012/185948185948On the Sets of Convergence for Sequences of the ๐-Bernstein Polynomials with ๐>1Sofiya Ostrovska0Ahmet Yaลar รzban1Department of Mathematics, Atilim University, Incek, 06836 Ankara, TurkeyDepartment of Mathematics, Atilim University, Incek, 06836 Ankara, TurkeyThe aim of this paper is to present new results related to the convergence of the sequence of the ๐-Bernstein polynomials {๐ต๐,๐(๐;๐ฅ)} in the case ๐>1, where ๐ is a continuous function on [0,1]. It is shown that the polynomials converge to ๐ uniformly on the time scale ๐๐={๐โ๐}โ๐=0โช{0}, and that this result is sharp in the sense that the sequence {๐ต๐,๐(๐;๐ฅ)}โ๐=1 may be divergent for all ๐ฅโ๐
โงต๐๐. Further, the impossibility of the uniform approximation for the Weierstrass-type functions is established. Throughout the paper, the results are illustrated by numerical examples.http://dx.doi.org/10.1155/2012/185948 |
| spellingShingle | Sofiya Ostrovska Ahmet Yaลar รzban On the Sets of Convergence for Sequences of the ๐-Bernstein Polynomials with ๐>1 Abstract and Applied Analysis |
| title | On the Sets of Convergence for Sequences of the ๐-Bernstein Polynomials with ๐>1 |
| title_full | On the Sets of Convergence for Sequences of the ๐-Bernstein Polynomials with ๐>1 |
| title_fullStr | On the Sets of Convergence for Sequences of the ๐-Bernstein Polynomials with ๐>1 |
| title_full_unstemmed | On the Sets of Convergence for Sequences of the ๐-Bernstein Polynomials with ๐>1 |
| title_short | On the Sets of Convergence for Sequences of the ๐-Bernstein Polynomials with ๐>1 |
| title_sort | on the sets of convergence for sequences of the ๐ bernstein polynomials with ๐ 1 |
| url | http://dx.doi.org/10.1155/2012/185948 |
| work_keys_str_mv | AT sofiyaostrovska onthesetsofconvergenceforsequencesoftheqbernsteinpolynomialswithq1 AT ahmetyasarozban onthesetsofconvergenceforsequencesoftheqbernsteinpolynomialswithq1 |