Abstract
In this paper we introduce a class of Bernstein–Durrmeyer operators with respect to an arbitrary measure ρ on the d -dimensional simplex, and a class of more general polynomial integral operators with a kernel function involving the Bernstein basis polynomials. These operators generalize the well-known Bernstein–Durrmeyer operators with respect to Jacobi weights. We investigate properties of the new operators. In particular, we study the associated reproducing kernel Hilbert space and show that the Bernstein basis functions are orthogonal in the corresponding inner product. We discuss spectral properties of the operators. We make first steps in understanding convergence of the operators.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
