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Approximation by Durrmeyer-type operators

Vijay Gupta, G. S. Srivastava (1996)

Annales Polonici Mathematici

We define a new kind of Durrmeyer-type summation-integral operators and study a global direct theorem for these operators in terms of the Ditzian-Totik modulus of smoothness.

Approximation by perturbed neural network operators

George A. Anastassiou (2015)

Applicationes Mathematicae

This article deals with the determination of the rate of convergence to the unit of each of three newly introduced perturbed normalized neural network operators of one hidden layer. These are given through the modulus of continuity of the function involved or its high order derivative that appears in the right-hand side of the associated Jackson type inequalities. The activation function is very general, in particular it can derive from any sigmoid or bell-shaped function. The right-hand sides of...

Approximation by q -Bernstein type operators

Zoltán Finta (2011)

Czechoslovak Mathematical Journal

Using the q -Bernstein basis, we construct a new sequence { L n } of positive linear operators in C [ 0 , 1 ] . We study its approximation properties and the rate of convergence in terms of modulus of continuity.

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