Abstract
In this paper we introduce two new Bernstein-type operators which are closely related to each other. The former is associated with the Pólya distribution and includes as a particular case the Bleimann-Butzer-Hahn operator. The second is associated with the inverse beta probability distribution. Approximation properties for both operators concerning rates of convergence, preservation of Lipschitz constants, and monotonic convergence under convexity are given. In dealing with the last two topics, probabilistic methods play an important role.
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