Smoothness Properties of Modified Bernstein-Kantorovich Operators - Özarslan, Mehmet Ali; Duman, Oktay (Taylor & Francis, 2016)
In this article, we consider modified Bernstein-Kantorovich operators and investigate their approximation properties. We show that the order of approximation to a function by these operators is at least as good as that of ones classically used. We obtain a simultaneous approximation result for our operators. Also, we prove two direct approximation results via the usual second-order modulus of smoothness and the second-order Ditzian-Totik modulus of smoothness, respectively. Finally, some graphical illustrations are provided.
Keywords: 41A36, modulus of continuity,; Bernstein-Kantorovich operators, simultaneous approximation; Ditzian-Totik modulus of smoothness, 41A25, MATHEMATICS, APPLIED; POSITIVE LINEAR-OPERATORS, APPROXIMATION PROPERTIES; modulus ofcontinuity, Ditzian-Totik modulus ofsmoothness