Abstract
ABSTRACTIn this article we construct a sequence of Stancu-type operators that are based on a function τ. This function is any function on [0,1] continuously differentiable ∞ times, such that τ(0) = 0, τ(1) = 1 and τ′(x)>0 for x∈[0,1]. Note that the Korovkin set is generalized to {1,τ,τ2} and these operators present a better degree of approximation then the original ones. We give a direct approximation theorem by means of the Ditzian-Totik modulus of smoothness and a Voronovskaja type theorem.
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