A study of generalized Gamma-type operators

Abstract

In this study, we discuss the approximation properties of Gamma operators $\mathbf{G}_{\alpha}$ for absolutely continuous and locally bounded functions by using results of probability theory and some inequalities with the method of Bojanic-Cheng. And then, metric form $\Omega_{u}(\xi,\lambda)$ is used with asymptotic formula combining to calculate an convergence rate asymptotically of Gamma operators $\mathbf{G}_{\alpha}$ for the bounded functions locally and also analysis techniques are used with Bojanic-Khan-Cheng's method to calculate an optimal convergence rate of Gamma operators $\mathbf{G}_{\alpha}$ for the functions which are absolutely continuous. Lastly, the convergence of the operators to a specific function is illustrated using Maple software.