| Title:
|
On Korovkin type theorem in the space of locally integrable functions (English) |
| Author:
|
Gadjiev, A. D. |
| Author:
|
Efendiyev, R. O. |
| Author:
|
Ibikli, E. |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
53 |
| Issue:
|
1 |
| Year:
|
2003 |
| Pages:
|
45-53 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
It is shown that a Korovkin type theorem for a sequence of linear positive operators acting in weighted space $L_{p,w}({\mathrm loc})$ does not hold in all this space and is satisfied only on some subspace. (English) |
| Keyword:
|
linear positive operators |
| Keyword:
|
Korovkin type theorem |
| Keyword:
|
weighted $L_p({\mathrm loc})$ spaces |
| MSC:
|
41A25 |
| MSC:
|
41A36 |
| MSC:
|
41A65 |
| idZBL:
|
Zbl 1013.41011 |
| idMR:
|
MR1961997 |
| . |
| Date available:
|
2009-09-24T10:58:48Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/127779 |
| . |
| Reference:
|
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| Reference:
|
[2] S. J. Bernau: Theorems of Korovkin type for $L^p$ spaces.Pacific J. Math. 53 (1974), 11–19. MR 0393979, 10.2140/pjm.1974.53.11 |
| Reference:
|
[3] K. Donner: Korovkin Theorems in $L^p$-spaces.J. Funct. Anal. 42 (1981), 12–28. MR 0620578, 10.1016/0022-1236(81)90046-X |
| Reference:
|
[4] V. K. Dzyadik: On the approximation of functions by linear positive operators and singular integrals.Mat. Sbornik 70 (1966), 508–517. (Russian) MR 0208243 |
| Reference:
|
[5] A. D. Gadziev: The convergence problem for a sequence of positive linear operators on unbounded sets, and Theorems analogous to that of P. P. Korovkin.Dokl. Akad. Nauk SSSR 218, no. 5. Zbl 0312.41013, MR 0367522 |
| Reference:
|
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| Reference:
|
[7] N. B. Haaser and J. A. Sullivan: Real Analysis.Dover Publications, INC, New York, 1991. MR 1088254 |
| Reference:
|
[8] W. Kitto and D. E. Walbert: Korovkin approximations in $L^p$-spaces.Pacific J. Math. 63 (1976), 153–167. MR 0417658, 10.2140/pjm.1976.63.153 |
| Reference:
|
[9] A. Kufner, O. John and S. Fučík: Function Spaces.Academia, Prague, 1977. MR 0482102 |
| Reference:
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[10] M. W. Muller: $L_p$-approximation by the method of integral Meyer-König and Zeller operators.Studia Math. 63 (1978), 81–88. MR 0508883, 10.4064/sm-63-1-81-88 |
| Reference:
|
[11] J. J. Swetits and B. Wood: Quantitative estimates for $L_p$-approximation with positive linear operators.J. Approx. Theory 38 (1983), 81–89. MR 0700880, 10.1016/0021-9045(83)90144-2 |
| Reference:
|
[12] J. J. Swetits and B. Wood: On degree of $L_p$-approximation with positive linear operators.J. Approx. Theory 87 (1996), 239–241. MR 1418496 |
| Reference:
|
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| . |
