Abstract

In this work we introduce for the first time the multivariate 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 multivariate modulus of continuity. We continue with the multivariate global smoothness preservation of these operators. We present extensively the related multivariate iterated approximation, as well as, the multivariate simultaneous approximation and their combinations. Using differentiability into our research, we are producing higher speeds of approximation, multivariate simultaneous global smoothness preservation is also studied.