In this article, we introduce a generalized form of the modified \(\alpha \) -Bernstein operators. We study their properties concerning approximation, convergence, and accuracy of the approximation error. We study the order of approximation of these operators by Voronovskaja type result and its error of approximation by several techniques of approximation theory. In the last part, we illustrate the impact of our generalization through the application of specific numerical and graphical examples by taking the different values of the introduced parameters to study their effects. By introducing shape parameters, we improved control and flexibility in approximation by these operators to use in practical areas such as image processing.
