Operators based on Polya distribution and finite differences

The several generalizations of the well-known Bernstein polynomials are available in the literature. The general form of Bernstein polynomial based on Polya distribution and its Kantorovich variant available in the literature have no links. In order to introduce a modification of a known operator, it is important to have some connection with the original one. Here, we provide a link between the such operators and its Kantorovich type integral variant using the method of backward difference operator and find another generalization, different than the one proposed before by Razi. We also provide some direct results for the Kantorovich operators. Finally, we also introduce the higher order Polya-Kantorovich operators.