Best Constants in Preservation Inequalities Concerning the First Modulus and Lipschitz Classes for Bernstein-Type Operators

AbstractWe consider families (Lt, t∈T) of positive linear operators such that eachLtis representable in terms of a stochastic process starting at the origin and having nondecreasing paths and integrable stationary increments. For these families, we give probabilistic characterizations of the best possible constants both in preservation inequalities concerning the first modulus and in preservation of Lipschitz classes of first order. As an application, we compute such constants for the Bernstein, Szász, Gamma, Baskakov, and Beta operators