In this paper, we give an overview of operators of Durrmeyer type with respect to arbitrary measure. Our construction includes the Bernstein-Durrmeyer operator, the Szász-Mirakjan-Durrmeyer operator, and the Baskakov-Durrmeyer operator with respect to arbitrary measure. We are particularly interested in the convergence of the operators. We discuss the uniform and the pointwise convergence as well as convergence in the corresponding weighted Lp -spaces. A new result is the statement on the Lp-convergence of the Szász-Mirakjan-Durrmeyer operator and the Baskakov-Durrmeyer operator without additional restrictions on the measure.
CITATION STYLE
Berdysheva, E. E. (2015). Operators of Durrmeyer type with respect to arbitrary measure. In Springer Proceedings in Mathematics and Statistics (Vol. 143, pp. 225–263). Springer New York LLC. https://doi.org/10.1007/978-81-322-2485-3_20
Mendeley helps you to discover research relevant for your work.