In this paper we introduce and study a sequence of Bernstein-Durrmeyer type operators $(M_{n,mu})_{ngeq 1}$, acting on spaces of continuous or integrable functions on the multi-dimensional hypercube $Q_d$ of $mathbf{R}^d$ ($dgeq 1$), defined by means of an arbitrary measure $mu$. We investigate their approximation properties both in the space of all continuous functions and in $L^p$-spaces with respect to $mu$, also furnishing some esitmates of the rate of convergence. Further, we prove an asymptotic formula for the $M_{n,mu}$'s. The paper ends with a concrete example.

A generalization of Bernstein-Durrmeyer operators on hypercubes by means of an arbitrary measure

Vita Leonessa
2019

Abstract

In this paper we introduce and study a sequence of Bernstein-Durrmeyer type operators $(M_{n,mu})_{ngeq 1}$, acting on spaces of continuous or integrable functions on the multi-dimensional hypercube $Q_d$ of $mathbf{R}^d$ ($dgeq 1$), defined by means of an arbitrary measure $mu$. We investigate their approximation properties both in the space of all continuous functions and in $L^p$-spaces with respect to $mu$, also furnishing some esitmates of the rate of convergence. Further, we prove an asymptotic formula for the $M_{n,mu}$'s. The paper ends with a concrete example.
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11563/136388
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