On a Chlodovsky variant of a multivariate beta operator

In this work, we state a Chlodovsky variant of a multivariate beta operator to be called hereafter the multivariate beta-Chlodovsky operator. We show that the multivariate beta-Chlodovsky operator can preserve properties of a general function of modulus of continuity and also the Lipschitz constant of a Lipschitz continuous function. Furthermore we set an H ω ( Δ ) class by the function of modulus of continuity ω and give some results for functions belonging to H ω ( Δ ) .