| Approximation by Modified Summation Integral Type Operators in the $L_p$ Spaces |
| Received:October 05, 2007 Revised:July 07, 2008 |
| Key Words:
Beta operators $K$-functional moduli of smoothness Riesz-Thorin interpolation theorem H\"{o}lder inequality.
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| Fund Project:the National Natural Science Foundation of China (No.10571040). |
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| Abstract: |
| The generalized summation integral type operators with Beta basis functions are widely studied. At present, the investigations for the properties of these operators are only limited to the functions of bounded variation. Some authors studied the rate of point-wise rate of convergence, asymptotic formula of Voronovskaja type, and some direct results about these type of operators. The present paper considers the direct, inverse and equivalence theorems of modified summation integral type operators in the $L_p$ spaces. |
| Citation: |
| DOI:10.3770/j.issn:1000-341X.2009.06.017 |
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