About some linear operators.
Our aim is to change classical test functions of Korovkin theorem on modular spaces by using -summability.
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.
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...
Using the -Bernstein basis, we construct a new sequence of positive linear operators in We study its approximation properties and the rate of convergence in terms of modulus of continuity.