Abstract
In this paper the iterates of the \(q\)-Durrmeyer operators are introduced using a modification. For these iterates the convergence results are obtained. The estimates for the rate of convergence are obtained in terms of the modulus of smoothness. A Voronovskaya type asymptotic result is obtained. Finally necessary conditions are derived which guarantee the convergence of these iterates to the projection operators.
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This work is carried out under the project on Optimization and Reliability Modelling of Indian Statistical Institute.
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Gairola, A.R., Deepmala & Mishra, L.N. Rate of Approximation by Finite Iterates of \(q\)-Durrmeyer Operators. Proc. Natl. Acad. Sci., India, Sect. A Phys. Sci. 86, 229–234 (2016). https://doi.org/10.1007/s40010-016-0267-z
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DOI: https://doi.org/10.1007/s40010-016-0267-z