Gamma-type operators and composition

Abstract In the present article, we examine the approximation properties of certain Gamma-type operators. Precisely, we consider the compositions of Rathore and Lupaş operators. We estimate the moments of the new composition operators and provide their probabilistic interpretation as well. Then, we provide some convergence results and their difference estimates, while focusing on the preservation of the moduli of smoothness of first- and second-order, using a stochastic approach. Additionally, Korovkin-type theorems and Voronovskaja-type asymptotic formulas are established for these operators. Finally, we consider graphical examples and their numerical interpretations to compare the speed of convergence for the composition operators and their components.