A generalization of Bernstein-Durrmeyer operators on hypercubes by means of an arbitrary measure
DOI:
https://doi.org/10.24193/subbmath.2019.2.09Keywords:
Bernstein operator, Bernstein-Durrmeyer operator, approximation process, asymptotic formula.Abstract
In this paper we introduce and study a sequence of Bernstein- Durrmeyer type operators (Mn,µ)n≥1, acting on spaces of continuous or inte- grable functions on the multi-dimensional hypercube Qd of Rd (d ≥ 1), defined by means of an arbitrary measure µ. We investigate their approximation proper- ties both in the space of all continuous functions and in Lp-spaces with respect to µ, also furnishing some estimates of the rate of convergence. Further, we prove an asymptotic formula for the Mn,µ’s. The paper ends with a concrete example.
Mathematics Subject Classification (2010): 41A36, 41A63, 41A10.
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