On mixed multidimensional exponential Kantorovich operators

In this paper, we introduce and study a family of multidimensional mixed exponential Kantorovich operators on the hypercube [0,1]^N. The idea is to define a vector of operators where the integral mean replaces the sample values of the function just with respect to a single variable, letting the exponential sampling-type structure for the other N-1 variables. For such operators, we compute the first multidimensional exponential moments and then we prove both pointwise and uniform convergence: the latter result is obtained by means of Korovkin type theorems. Furthermore, we prove a quantitative estimate of the order of approximation in terms of the modulus of continuity of the approximated function.