On Stancu-Mühlbach Operators and Some Connected Problems Concerning Probability Distributions Original Research Article

New approximation properties concerning Beta and Stancu-Mühlbach operators are given. It is shown that both operators preserve Lipschitz constants. We also give quantitative estimates for the approximation of Bernstein, Szász, and Baskakov operators by Stancu-Mühlbach operators, as well as for the approximation of Gamma operators by Beta operators. By duality, these results may be translated into quantitative estimates for the total variation distance from the Pólya distribution to the binomial, Poisson, and negative binomial distributions.