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In this work, we construct the genuine Durrmeyer–Stancu type operators depending on parameter α in [ 0 , 1 ] $[0,1]$ as well as ρ > 0 $\rho >0$ and study some useful basic properties of the operators. We also obtain Grüss–Voronovskaja and quantitative Voronovskaja types approximation theorems for the aforesaid operators. Further, we present numerical and geometrical approaches to illustrate the significance of our new operators.

Approximation of functions by a class of Durrmeyer–Stancu type operators which includes Euler’s beta function