Abstract
It is well-known that, for positive linear operators, if f″(x)≠0 the best rate of convergence is n−1 even though there exists higher order derivatives of f(x). In this paper, we present a new way to construct a class of linear operators {Ln,r(f,x):r≥2}. We show that, for Ln,r(f,x), the rate of convergence is improved with the existence of higher order derivatives. Simultaneous approximation is also studied.
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