Approximation Properties of the Modified Stancu Operators. (4th March 2017) - Acu, Ana Maria; Agrawal, P. N.; Neer, Trapti
ABSTRACT: In 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, τ 2 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.