A modification of bernstein-kontorovich polynomials ona symmetric interval

In general, in this study, the approximation properties of the operator N_ծ (f;u), which is a sequence of Linear Positive Operators, are examined and their basic properties are examined. The smooth approximation of our operator is shown using Korovkin's theorem. By examining previous studies, the approximation of the operator, which we obtained a generalization, is examined for functions that satisfy the approximation speed, Voronowskaja type asymptotic approximation and Lipschitz condition. The approximation properties of the operator N_ծ (f;u) are examined. The approximation of different functions for the given operator is shown with the help of graphics. If a selected function is a function, the numerical values of the approximation of the operator N_ծ (f;u) to a function are found for some values of " ծ " and "u", and the values found are prepared as a table. Keywords: Bernstein polynomial, Bernstein-Kantorovich polynomials, Korovkin theorem, rate of approximation, linear positive operator