Abstract
We consider a special knot sequence ui+1=qui+1 and define a one parameter family of Bernstein–Schoenberg operators. We prove that this operator converges to f uniformly for all f in C[0,1]. This operator also inherits the geometric properties of the classical Bernstein–Schoenberg operator. Moreover we show that the error function Em,n has a particular symmetry property, that is Em,n(f;x;q)=Em,n(f;1−x,1/q) provided that f is symmetric on [0,1].
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