Approximation by symmetrized and perturbed hyperbolic tangent activated convolutions as positive linear operators

In this work, we studied further the univariate symmetrized and perturbed hyperbolic tangent activated convolution type operators of three kinds. Here, this is done with the method of positive linear operators. Their new approximation properties are established by the quantitative convergence to the unit operator using the modulus of continuity. It is also studied the related simultaneous approximation, as well as the iterated approximation.