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positive linear operator; Bernstein-type operator; genuine Bernstein-Durrmeyer operator; simultaneous approximation; degree of approximation; moduli of continuity
We introduce and study a one-parameter class of positive linear operators constituting a link between the well-known operators of S. N. Bernstein and their genuine Bernstein-Durrmeyer variants. Several limiting cases are considered including one relating our operators to mappings investigated earlier by Mache and Zhou. A recursion formula for the moments is proved and estimates for simultaneous approximation of derivatives are given.
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