Convergence properties of new α-Bernstein–Kantorovich type operators

Abstract

In the present paper, we introduce a new sequence of α-Bernstein-Kantorovich type operators, which fix constant and preserve Korovkin’s other test functions in a limiting sense. We extend the natural Korovkin and Voronovskaja type results into a sequence of probability measure spaces. Then, we establish the convergence properties of these operators using the Ditzian-Totik modulus of smoothness for Lipschitz-type space and functions with derivatives of bounded variations. © The Indian National Science Academy 2024.