Direct and converse inequalities for positive linear operators on the positive semi-axis
1999 ◽
Vol 66
(1)
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pp. 90-103
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Keyword(s):
AbstractWe consider positive linear operators of probabilistic type L1f acting on real functions f defined on the positive semi-axis. We deal with the problem of uniform convergence of L1f to f, both in the usual sup-norm and in a uniform Lp type of norm. In both cases, we obtain direct and converse inequalities in terms of a suitable weighted first modulus of smoothness of f. These results are applied to the Baskakov operator and to a gamma operator connected with real Laplace transforms, Poisson mixtures and Weyl fractional derivatives of Laplace transforms.
2015 ◽
Vol 69
(3-4)
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pp. 359-367
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2014 ◽
Vol 96
(110)
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pp. 159-168
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Keyword(s):
2021 ◽
Vol 7
(1)
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pp. 134-172
2008 ◽
Vol 3
(2)
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2010 ◽
Vol 47
(3)
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pp. 289-298
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