On a new Kantorovich operator based on Hermite polynomials (Q6584793)

The authors in this study generalized Kantorovich variant of operators based on Hermite polynomials of three variables. They computed the moment generating function of the operator and discussed direct results associated to it. They examined the quantitative asymptotic formula and convergence estimates in terms of modulus of continuity. Further, they graphically shown the convergence rate of the operator. A new discrete operator has also been defined based on the composition of Hermite Kantorovich and Szász-Mirakyan operator. For this new composition, they studied some direct results and Voronovskaja theorem in the weighted space.