Approximation by parametrized logistic activated convolution type operators

In this work we introduce for the first time the univariate parametrized logistic activated convolution type operators in three kinds. We present their approximation properties, that is the quantitative convergence to the unit operator via the modulus of continuity. We continue with the global smoothness preservation of these operators. We present extensively the related iterated approximation, as well as, the simultaneous approximation and their combinations. Including differentiability and fractional differentiabily into our research, are producing higher speeds of approximation. Simultaneous global smoothness preservation is also treated.