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...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Hindawi Limited
2019-01-01
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| Series: | Journal of Function Spaces |
| Online Access: | http://dx.doi.org/10.1155/2019/2329060 |
| Summary: | 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. |
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| ISSN: | 2314-8896 2314-8888 |