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Convergence of iterates of genuine and ultraspherical Durrmeyer operators to the limiting semigroup: -estimates |
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| Authors: | Heiner Gonska, Margareta Heilmann,Ioan Ra a |
| Affiliation: | aDepartment of Mathematics, University of Duisburg-Essen, Forsthausweg 2, D-47057 Duisburg, Germany;bFaculty of Mathematics and Natural Sciences, University of Wuppertal, Gaußstraße 20, D-42119 Wuppertal, Germany;cDepartment of Mathematics, Technical University, Str. C. Daicoviciu, 15, RO-400020 Cluj-Napoca, Romania |
| Abstract: | In the present note a general inequality for the degree of approximation of semigroups by iterates of commuting bounded linear operators on Banach spaces is given. Combining this with a recent quantitative Voronovskaja-type result applications to Durrmeyer operators with ultraspherical weights are derived. Our considerations include the genuine Bernstein–Durrmeyer operators. |
| Keywords: | Operators on Banach spaces Semigroup Bernstein– Durrmeyer operators with ultraspherical weights Degree of approximation Genuine Bernstein– Durrmeyer operators Moduli of smoothness |
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