On Sequences of J. P. King-Type Operators
This survey is devoted to a series of investigations developed in the last fifteen years, starting from the introduction of a sequence of positive linear operators which modify the classical Bernstein operators in order to reproduce constant functions and x2 on [0,1]. Nowadays, these operators are k...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2019-01-01
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| Series: | Journal of Function Spaces |
| Online Access: | http://dx.doi.org/10.1155/2019/2329060 |
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| _version_ | 1832549370184073216 |
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| author | Tuncer Acar Mirella Cappelletti Montano Pedro Garrancho Vita Leonessa |
| author_facet | Tuncer Acar Mirella Cappelletti Montano Pedro Garrancho Vita Leonessa |
| author_sort | Tuncer Acar |
| collection | DOAJ |
| description | This survey is devoted to a series of investigations developed in the last fifteen years, starting from the introduction of a sequence of positive linear operators which modify the classical Bernstein operators in order to reproduce constant functions and x2 on [0,1]. Nowadays, these operators are known as King operators, in honor of J. P. King who defined them, and they have been a source of inspiration for many scholars. In this paper we try to take stock of the situation and highlight the state of the art, hoping that this will be a useful tool for all people who intend to extend King’s approach to some new contents within Approximation Theory. In particular, we recall the main results concerning certain King-type modifications of two well known sequences of positive linear operators, the Bernstein operators and the Szász-Mirakyan operators. |
| format | Article |
| id | doaj-art-3d3e8950973c42f291934356cd794e37 |
| institution | Kabale University |
| issn | 2314-8896 2314-8888 |
| language | English |
| publishDate | 2019-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces |
| spelling | doaj-art-3d3e8950973c42f291934356cd794e372025-02-03T06:11:27ZengWileyJournal of Function Spaces2314-88962314-88882019-01-01201910.1155/2019/23290602329060On Sequences of J. P. King-Type OperatorsTuncer Acar0Mirella Cappelletti Montano1Pedro Garrancho2Vita Leonessa3Department of Mathematics, Faculty of Science, Selcuk University, Selcuklu, Konya, TurkeyDepartment of Mathematics, University of Bari, Bari, ItalyDepartment of Mathematics, University of Jaén, Jaén, SpainDepartment of Mathematics, Computer Science and Economics, University of Basilicata, Potenza, ItalyThis survey is devoted to a series of investigations developed in the last fifteen years, starting from the introduction of a sequence of positive linear operators which modify the classical Bernstein operators in order to reproduce constant functions and x2 on [0,1]. Nowadays, these operators are known as King operators, in honor of J. P. King who defined them, and they have been a source of inspiration for many scholars. In this paper we try to take stock of the situation and highlight the state of the art, hoping that this will be a useful tool for all people who intend to extend King’s approach to some new contents within Approximation Theory. In particular, we recall the main results concerning certain King-type modifications of two well known sequences of positive linear operators, the Bernstein operators and the Szász-Mirakyan operators.http://dx.doi.org/10.1155/2019/2329060 |
| spellingShingle | Tuncer Acar Mirella Cappelletti Montano Pedro Garrancho Vita Leonessa On Sequences of J. P. King-Type Operators Journal of Function Spaces |
| title | On Sequences of J. P. King-Type Operators |
| title_full | On Sequences of J. P. King-Type Operators |
| title_fullStr | On Sequences of J. P. King-Type Operators |
| title_full_unstemmed | On Sequences of J. P. King-Type Operators |
| title_short | On Sequences of J. P. King-Type Operators |
| title_sort | on sequences of j p king type operators |
| url | http://dx.doi.org/10.1155/2019/2329060 |
| work_keys_str_mv | AT tunceracar onsequencesofjpkingtypeoperators AT mirellacappellettimontano onsequencesofjpkingtypeoperators AT pedrogarrancho onsequencesofjpkingtypeoperators AT vitaleonessa onsequencesofjpkingtypeoperators |