Approximation of the semi-infinite interval
The approximation of a function f∈C[a,b] by Bernstein polynomials is well-known. It is based on the binomial distribution. O. Szasz has shown that there are analogous approximations on the interval [0,∞) based on the Poisson distribution. Recently R. Mohapatra has generalized Szasz' result to t...
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| Format: | Article |
| Language: | English |
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Wiley
1980-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
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| Online Access: | http://dx.doi.org/10.1155/S0161171280000580 |
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| _version_ | 1832555032630788096 |
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| author | A. McD. Mercer |
| author_facet | A. McD. Mercer |
| author_sort | A. McD. Mercer |
| collection | DOAJ |
| description | The approximation of a function f∈C[a,b] by Bernstein polynomials is well-known. It is based on the binomial distribution. O. Szasz has shown that there are analogous approximations on the interval [0,∞) based on the Poisson distribution. Recently R. Mohapatra has generalized Szasz' result to the case in which the approximating function is αe−ux∑k=N∞(ux)kα+β−1Γ(kα+β)f(kαu)The present note shows that these results are special cases of a Tauberian theorem for certain infinite series having positive coefficients. |
| format | Article |
| id | doaj-art-298689714f05450f9173148e48621ebd |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1980-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-298689714f05450f9173148e48621ebd2025-02-03T05:49:42ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251980-01-013479379610.1155/S0161171280000580Approximation of the semi-infinite intervalA. McD. Mercer0Department of Mathematics and Statistics, University of Guelph, Ontario, Guelph, CanadaThe approximation of a function f∈C[a,b] by Bernstein polynomials is well-known. It is based on the binomial distribution. O. Szasz has shown that there are analogous approximations on the interval [0,∞) based on the Poisson distribution. Recently R. Mohapatra has generalized Szasz' result to the case in which the approximating function is αe−ux∑k=N∞(ux)kα+β−1Γ(kα+β)f(kαu)The present note shows that these results are special cases of a Tauberian theorem for certain infinite series having positive coefficients.http://dx.doi.org/10.1155/S0161171280000580Szasz operatorsBorel summabilityTauberian theorems. |
| spellingShingle | A. McD. Mercer Approximation of the semi-infinite interval International Journal of Mathematics and Mathematical Sciences Szasz operators Borel summability Tauberian theorems. |
| title | Approximation of the semi-infinite interval |
| title_full | Approximation of the semi-infinite interval |
| title_fullStr | Approximation of the semi-infinite interval |
| title_full_unstemmed | Approximation of the semi-infinite interval |
| title_short | Approximation of the semi-infinite interval |
| title_sort | approximation of the semi infinite interval |
| topic | Szasz operators Borel summability Tauberian theorems. |
| url | http://dx.doi.org/10.1155/S0161171280000580 |
| work_keys_str_mv | AT amcdmercer approximationofthesemiinfiniteinterval |