Abstract
For linear combinations of Gamma operators, if 0<a<2r,\(\frac{1}{2} - \frac{1}{{2r}} \leqslant \lambda \leqslant 1\), or\(0 \leqslant \lambda< \frac{1}{2} - \frac{1}{{2r}}(r \geqslant 2)\),\(0< a< \frac{{r + 1}}{{1 - \lambda }}\), we obtain an equivalent theorem with
instead of
, where
is the Ditzian-Totik moduli of smoothness.
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References
Ditzian, Z. and Totik, V., Moduli of Smoothness, Springer-Verlag, New York, 1987.
Totik, V., The Gamma Operators inLp Spaces, Publ. Math. (Debrecen), 32(1985), 43–55.
Ditzian, Z., Direct Estimate for Bernstein Polynomials, J. Approx. Theory, 79(1994), 165–166.
Guo, S., ect, Pointwise Estimate, for Szász-Type Operators, J. Approx. Theory, 94(1998), 160–171.
Ditzian, Z., Rate of Approximation of Linear Processes, Acta Sci. Math., 48(1985), 103–128.
Guo, S., ect, Pointwise Approximation for Linear Combinations of Bernstein Operators, J. Approx. Theory, 107(2000), 109–120.
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Supported by the Hebei Provincial Natural Science Foundation of China (101090).
Suported by the Major Subject Foundation of Hebei Normal University.
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Shunsheng, G., Qiulan, Q. On pointwise estimate for Gamma operators. Approx. Theory & its Appl. 18, 93–98 (2002). https://doi.org/10.1007/BF02837117
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DOI: https://doi.org/10.1007/BF02837117