Inverse beta and generalized Bleimann-Butzer-Hahn operators
The authors introduce two new Bernstein-type operators acting on \([0,\infty]\) which are closely related to each other. The former is associated with a Pólya distribution and includes as a particular case the Bleimann-Butzer-Hahn operator. The second is associated with the inverse beta probability distribution. The authors also study approximation properties for both operators concerning rates of convergence, preservation of Lipschitz constants, and monotonic convergence under convex functions. For the last two topics, the author shows in a novel way how probabilistic methods play an important role.
scientific article; zbMATH DE number 502997