Theoretical Validation and Comparative Analysis of Higher Order Modified Bernstein Operators

In this study, we present a technique for enhancing the order of approximation of the modified form of the Bernstein operators that Usta F. achieved. Moreover, two novel operators with degrees of approximation one and two are obtained. Furthermore, we validate a few theoretical findings such as the Korovkin theorem, Voronovskaja theorem, modulus of continuity, etc. about the rate of convergence of these operators. In the end, we operate graphs and tables to illustrate the comparison between the constructed operators and compute the numerical verification of the theoretical conclusions.